Villain is 35/5/0 after 20 hands, so no other reads

PokerStars No-Limit Hold'em, $0.05 BB (6 handed) - PokerStars Converter Tool from FlopTurnRiver.com

Hero (CO) ($9.65)
Button ($4.22)
SB ($5.04)
BB ($3.68)
UTG ($5.07)
MP ($5.12)

Preflop: Hero is CO with Q, K
2 folds, Hero bets $0.20, 2 folds, BB calls $0.15

Flop: ($0.42) 5, K, Q (2 players)
BB bets $0.35, Hero raises to $1.20, BB calls $0.85

good flop for me, and he donk bets. rangewise, i think he has a lot of Kx or Qx

Turn: ($2.82) 9 (2 players)
BB checks, Hero ???

hmm.... so now what? he's got less than the pot behind. shove?