Yes, age and rookie status don't always go hand in hand - Dick Grayson was a veteran at 15, as were several other sidekicks. So that does raise the issue of when she first debuted as a hero v. when she came to the US and met all the heroes we know. Not that I think of her as having been a tween hero.
I don't recall getting a "rookie" vibe from her in her first appearance, either. Though, to be fair, back then almost no adult hero ever seemed the rookie, even when we knew for a fact it was one of their fist five missions. Neither did any of the teens that I can think of, to be honest. Even if I did, I think once someone has two years (at max) under his/her belt, they are a veteran rather than rookie. Partially because it would get really annoying to see them making rookie mistakes for the 15 years real-time it would take for two years comic time to pass.