Even if she hadn't said that, it would be worth looking into what she likes or dislikes and finds easy or difficult. But the above isn't too specific and could refer to any combination of many problems.
Try to find out what she doesn't like about this job and which parts she finds too difficult and, more importantly, how you can help.
Many of the above questions are quite similar and may have the same answer, but it could make sense to ask different variants to approach it from different angles to get a more complete picture of her motivations and desires. You can pick or choose what makes sense to ask or skip, what to expand on or what else to ask, especially given her answers or what you already know. This may include just dropping it completely if she's not at all open to talking about it.
Mentoring, so the hard parts become easier and more enjoyable.
A second look at what she's actually doing.
In some cases people might end up doing a lot more than they're supposed to (which can certainly make things harder and less enjoyable) because they don't delegate or they aren't too clear on where exactly their responsibilities end.
Time to adjust.
Starting a new job can be quite stressful and sometimes all the changes can be overwhelming.
If you suspect this is the problem, you shouldn't tell her to just give it time, because that's a bit dismissive and, even if it's the best suggestion, it's not really what someone in that position wants to hear. Instead, you could delay making any decisions a bit (with her consent), try to help her adjust, have regular meetings to check in to see how she's settling in and provide any other support she may need.
Even if this isn't the problem, it might also be worth thinking how this is handled in future (or even in her case). Maybe there should be a slower transition into the role, where responsibilities are incrementally gained instead of suddenly changed (and actually moving roles is almost just a title change and a salary bump). This would also give her a better idea of what to expect in the new role before moving to it and could help her decide whether she even wants to move.
Confidence.
She may feel she doesn't have the required skills, even if she's exceeding expectations. See also: Imposter syndrome. This would likely also mean she's not enjoying it and thinks it's too hard.
Honest performance evaluations might help here. Give her praise when deserved, but also give her constructive criticism. Criticism is helpful for improving, obviously, but it can also make the praise seem more sincere.
Although how to deal with this specific aspect from a management perspective can probably be a question all by itself.
More focused or personalised responsibilities.
Perhaps you could move away some responsibilities she doesn't like and/or give her back some of her old responsibilities so she's still largely filling the new role, but actually enjoying it.
Or maybe she just has too many responsibilities and can't get them all done in a 40-hour week. It might be because the role itself is too broad, but it might also just be because it's new for her. In either case, the responsibilities should be reduced (permanently in the first case and temporarily in the second case) so it's more manageable.
Help dealing with specific tasks.
It might be that her responsibilities overall are not a problem, she just has problems dealing with specific instances of those responsibilities.
Perhaps her new job involves dealing with a particularly difficult individual, having many unnecessary meetings, working with painfully inefficient software or even moving to a different desk with a less pleasant environment (which can concern anything from her neighbours to the temperature and lighting to where she sits).
These should all be problems solvable in ways that doesn't involve fundamentally changing her overall responsibilities.
While in some cases someone might raise concerns if one of these things are bothering them, it may not apply to all such problems, she might feel it's a fundamental part of the job or there are too many individual problems and can't (all) be fixed, she may have already raised concerns but to someone else or you may not have realised this is potentially why she wants a demotion or she may simply not feel comfortable raising concerns in general.
A new promotion path.
This is an extension of giving more personalised responsibilities. If there are simply too many responsibilities she doesn't like in the new role, it might make sense to rethink how promotions work and how people move up in your company (especially if this is the only way she can move up).
Perhaps there's another way she can become more senior. In Software Development, for example, the traditional path involves everyone ending up as people managers, but a number of companies (especially the big tech companies) also have career paths that are still very technical. This might be more focused on solving more challenging problems or leading technical and architecture development. Such roles may still involve a bit of people management, but focuses on bringing value to the company more through technical expertise than management expertise.
A raise.
She might've been pushing for the position because she simply wanted a raise and this seems like (or is) the only or best way to get it.
Company policy and politics could get in the way of paying people what they're worth to the company. If you'd have to pay significantly more money to get someone else to do what she was doing in her previous role, just give her that money in the form of a raise instead.
To stay in her old job.
It might be that none of the above points apply and she just doesn't want any more responsibilities. She just wants to settle in to an easy job and stay there. Or she doesn't want to become more senior because the only way for her to do so is to remove things she enjoys and add things she dislikes.
Some employers don't like this and want everyone to move up (or leave), but these employees enjoy their current job and can be relied upon to consistently do a good job and be fairly loyal (because, for similar reasons, they also wouldn't want to go through the hassle of starting a new job).
If she was forced into the role, wanting to settle in is much more likely. Although, if she was the one who wanted the role, it might also be that she simply didn't quite know what she was getting herself into.
If difficulty is the problem: Of course harder things can also become easier over time, so it may also make sense to consider a slower career progression for her, which just involves slowly gaining or changing responsibilities without much pressure to suddenly have to do a bunch of new and difficult things. Although this should come with regular check-ins (which are generally a good idea anyway) to make sure she actually likes her current role at any given point in time and where her career is headed with any new responsibilities.
