Your 3-bet was way too small. It's not even a true min-bet.
Wait...why are you min raising with QQ there? Min raising tells
you nothing/gets you nowhere here. No value, no protection, no range on opponents hand. Nada...except it inflates the pot and invites people along. Even if the opponent raise to 600 with J5, they're calling an extra 471 to see a flop. Unless they're dumb and they fold there...
With that said, you just got a bit unlucky to run into pair vs bigger pair. You still would've rain into it if I had reraised bigger. So, just chalk it up to bad luck. Still, raise more preflop because there a ton of hands <KK that call there and you beat. So, take them to value town.