It's up to you.
If you feel you could get the raise, do it. Have your reasoning ready to explain.
I was in a consulting role once at an org where each person was doing the same work, on my team, and were billing the clients the same rate. I was being paid roughly 30% of what the others on the team were, as I was less experienced at the time i was hired (but still fully proficient).
6-7 months in, I had demonstrated I was able to do the same work as my peers, and had even innovated and built out ways to automated much of the work we were doing, making the entire team more productive and improving the number of hours we were billing out for.
I asked for a 50% raise, to a point where I'd still be behind the other team members who had more experience, but would be at a point that was much more reasonable and less likely to get me poached off somewhere else. My manager wasn't able to make the decision (usually has to be cleared by higher ups), but I received a phone call later that day saying it had been approved and they were very enthusiastic about how i'd been doing etc.
So really, it depends. if you have the ability to back it up, you should ask. Especially if you were being underpaid before - Basing pay on %'s from prior pay only continues a low pay situation, it doesn't take into account what you're worth.
Side note - The position I was in when this happened, I had started out 50% higher than the job I was at prior to it, where i'd asked for small raises several times and been denied and gaslit about why I wouldn't get it. But when I had the offer for this new place, all of a sudden, 30 seconds later they were offering to match it and were saying they'd been eyeing me for a supervisor role...
If it's very important, the last resort is to get an offer somewhere else and negotiate as a counter offer to stay at the company... but it may be better off to find another gig anyways. The saying is, if you want more money, you have to job hop.
To answer your other question though - asking for a raise after 6 months is not unprofessional. It's only unprofessional if it's for childish or invalid reasons...
By this I mean, your reasons for the raise can't be "I found out Scott is making 100k, we should be getting paid the same", and also shouldn't be "Target pays people $15/hr just for showing up." It should be focused on the value you provide to the business, perhaps the change in your workload and responsibilities (For example maybe that they're shouldering management of other employees onto you, and you hadn't been aware of that / signed up for that when you took the job, now it's a different job than it was before)