I'm interested in helping interview others, because I enjoy interacting with people and also setting a higher standard at my company.
This seems like a bit of a non-sequitur - interacting with someone "normally" is very different to interacting with them in an interview setting. You're trying to (in a very limited timeframe) form an accurate assessment of their skills, work out if they'd be a good fit for the team, and determine how much you think their experience is worth financially. You need to do all of that whilst, ideally, remaining polite and friendly to put them at ease (ie. not just barking questions at them one after the other.)
It's a very particular skillset that a lot of people (sadly even people that do this job on a regular basis!) aren't very good at.
However, I am relatively new, and one of the HR staff had said its a 'little early', which is quite vague.
I assume you've not been assigned to a managerial type role where it'd normally be your job to interview candidates, otherwise this would be weird. If you're the engineering manager, CTO, even lead developer of a team and they don't want you getting a look-in at anyone who would be working under you, they may have misunderstood your role.
Assuming the above isn't the case, then it's deliberately vague as there's no set timescale (or no guarantee it would ever be appropriate.) If you're a more junior or mid-level dev then it's unlikely they'd ask you to be on the interview panel unless:
- You've proven yourself to be one of the experts in a particular framework / library / technology, and they want to explicitly hire people to work with it;
- You're leaving after a while, and they want you to help interview your replacement;
- As above, but instead of leaving you're being promoted to a more senior position;
- You've shown yourself to be a good mentor and interact well with new hires, they'd like that to continue, and therefore they want you to form an opinion of potential new hires;
- They're down a person and want to draft "anyone" else in.
As above, there's no set timescale for any of that to happen. Your best bet if you really want to take part in interviews is to work your way up to a senior position quickly where you'll be drafted in to help as a matter of course - but in isolation, that would be a bit of an unusual career motivator!