$5 NLHE 6-max: Set mining with QQ?

Should have i just folded preflop?Bet the flop c\c or c\f like i did here.

full tilt poker $5.00 No Limit Hold'em - 6 players - View hand 1192302
DeucesCracked Poker Videos Hand History Converter

BB: $13.73
Hero (UTG): $5.00
MP: $1.83
CO: $5.20 16\12\4 villain 3bet 1 time out of 112 times prior to this hand
BTN: $5.90
SB: $8.20

Pre Flop: ($0.07) Hero is UTG with Q :club: Q :heart:
Hero raises to $0.15, 1 fold, CO raises to $0.52, 2 folds, BB calls $0.47, Hero calls $0.37

Flop: ($1.58) A :heart: J :heart: 8 :club: (3 players)
BB checks, Hero checks, CO bets $1.20, BB folds, Hero folds

Final Pot: $1.58
CO wins $1.48
(Rake: $0.10)

112 hand isn't enough for me not to 4bet PF here, especially with BB throwing dead money into the pot. As played, c/f the flop is fine.

Don't set-mine is 3-bet pots. As played, read the flop. What hands that villain 3-bets with do you beat? The only one I can think of here is KQ, and villain may not even 3-bet those.... so yeah, what should you do?

shove arr-in cuz he obviously has TT amirite