stars $50 - how much to bet heads up with set?

[JSampras1]

I'm still kind of new at NL, and my bet sizing sucks a lot of the time. I won the hand here, but I'm just wondering if i made a mistake in my bet sizes.

This is villain's second hand, so i had no stats. I think maybe i should have raised more on the flop, as there are draws that could call. I figure i bet a little less than half his stack on the turn, and push on the river. Betting the pot is more than half his stack, so i figured i would go a little light. As played was my turn bet too small? Too big? Not bad?

PokerStars No-Limit Hold'em, $0.50 BB (8 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Button ($49.45)
SB ($30.25)
Hero ($53.15)
UTG ($31.90)
UTG+1 ($25.90)
MP1 ($46.80)
MP2 ($49.25)
CO ($9.25)

Preflop: Hero is BB with Q[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">6 folds</font>, SB completes, <font color="#CC3333">Hero raises to $2</font>, SB calls $1.50.

Flop: ($4) K[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets $1.5</font>, <font color="#CC3333">Hero raises to $5</font>, SB calls $3.50.

Turn: ($14) T[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $9</font>, SB folds.