Nl50sh QQ vs nit

PartyGaming - $0.50 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

UTG: $58.67
Hero (CO): $63.79
BTN: $51.97 (VPIP: 16.46, PFR: 11.81, 3Bet Preflop: 6.06, Hands: 239)
SB: $66.44
BB: $56.10
SB posts SB $0.25, BB posts BB $0.50

Pre Flop: (pot: $0.75) Hero has Q♠ Q♦

fold, Hero raises to $1.50, BTN raises to $5.00, fold, fold, Hero calls $3.50

Flop: ($10.75, 2 players) 8♥ 6♠ T♦
Hero checks, BTN bets $5.50, Hero calls $5.50

Turn: ($21.75, 2 players) 9♣
Hero checks, BTN bets $10.33, fold

Villain 3bet BTNvsCO 0 (0/12), overall 3bet 5%,

Seems very nitty so I didnt like to 4bet/call.

Postflop my plan is to call flop and hope for villain to give up on turn. Seems like a bad plan.