NL4; SH: QQ against fish minraise + multitabler 3bet

IPoker, $0.02/$0.04 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

CO: $2.14 (53.5 bb)
BTN: $4.29 (107.3 bb)
Hero (SB): $4 (100 bb)
BB: $5.24 (131 bb)
UTG: $2.16 (54 bb)
MP: $2.39 (59.8 bb)

Preflop: Hero is SB with Q Q
UTG folds, MP raises to $0.08, CO calls $0.08, BTN raises to $0.24, Hero raises to $0.72, BB folds, MP calls $0.64, 2 folds

Flop: ($1.80) 4 A 5 (2 players)
Hero checks, MP bets $0.08, Hero calls $0.08

Turn: ($1.96) 5 (2 players)
Hero checks, MP bets $0.16, Hero calls $0.16

River: ($2.28) 8 (2 players)
Hero checks, MP checks

Results: $2.28 pot ($0.15 rake)
Final Board: 4 A 5 5 8
Hero mucked Q Q and won $2.13 ($1.17 net)
MP showed 7 7 and lost (-$0.96 net)

The initial raiser has the following stats: VP/PFR/AF/hands 71/41/6.0/17
The cold caller's stats: VP/PFR/AF/hands 37/17/3.3/46
The multitabler's stats: VP/PFR/AF/3bet/hands 24/18/0.9/8.3/97

I understand that the multitabler could be 3betting here a little bit looser than usual because the minraiser is a pretty large fish, as is the cold caller, so I guess that we just have to raise this one, but I'm not sure about how close this could be.

Postflop: I think I made a mistake. I should have pushed as the fish does not necessarily have to have an Ax hand. He could have a worse PP that he might even call on this board.