Yes, if she was born in mid-July, I'd hold off on breeding her too; at three months of age and 4.5lbs, it sounds like she could use a bit more time. But
@ladysown is right - they can get hormonal pretty early, and I've had a 12-week-old buck sire a litter (accidentally - he was
quite motivated!).
It looks like she is living with another doe - if you have the space, you might try putting her in her own cage. Does can be territorial and maybe she's just wound up from the battle for, or the maintenance of, the social hierarchy. And, like a friend who spent some time in jail as a young man says: isolation goes a long way toward changing an attitude.
The other thing to think about is that if she's really comfortable and confident from lots of handling by your daughter, she might think she's the alpha, even over humans. A little training might help with that. There's a full discussion of this on this thread:
https://rabbittalk.com/threads/help-rabbit-is-attacking-me.35974/page-2#post-350570
Like
@hotzcatz says, temperament is strongly related to genetics, but I have some of the sweetest does ever who still went through an uppity phase as they hit sexual maturity. It's the only temperament pass I give; in any other case, a truly aggressive or even unfriendly rabbit is designated by my kids as a "pot bunny."