QQ preflop line

[Alpha13]

Hero: $27
UTG: $13


25NL 6 max and I have QQ in MP. UTG limps and I raise $1, folded around to UTG who reraises to $3. I minraise to $5.75,he minraises back, 3 more raises and he is all in.

Tricky spot to be in with QQ, I think its only a coinflip against AK and there's a good chance villian holding AA/KK. But he's also a short stack stack which is why I only minraised (because I felt him coming over the top against say an $8 4bet would force me to call anyways, and the larger bet folds worse hands)

Well that was my thought process. I have a feeling you guys will tell me to reraise a larger amount, if so please tell me why

Thanks