QQ - Co vs BB on wet board

PokerStars - $0.05 NL (6 max) - Holdem - 6 players
Hand converted by Holdem Manager 3

Hero (CO): $5.00 (100 bb)
BTN: $5.00 (100 bb)
SB: $9.47 (189.4 bb)
BB: $6.06 (121.2 bb)
UTG: $5.86 (117.2 bb)
MP: $7.50 (150 bb)

SB posts $0.02, BB posts $0.05

Pre Flop: (pot: $0.07) Hero has Q♦: Q♥:
2 folds, Hero raises to $0.15, 2 folds, BB calls $0.10

standard raise

Flop: ($0.32, 2 players) 5♦: 8♦: 4♣:
BB bets $0.19, Hero calls $0.19

I guess a better line would be to raise the donk here to protect against draws

Turn: ($0.70, 2 players) 9♦:
BB bets $0.25, Hero calls $0.25

the way how I played flop, I should have raised here to protect at least against that straight draw - is this correct?

River: ($1.20, 2 players) 6♥:
BB bets $0.90, Hero folds

all the draws came and the price is too big

Results: $1.20 pot ($0.05 rake)
Final Board: 5♦: 8♦: 4♣: 9♦: 6♥:

BB wins $1.15