PokerStars No-Limit Hold'em, $0.05 BB (9 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

CO ($1.88)
Button ($3)
SB ($4.61)
Hero ($15.83)
UTG ($7.49)
UTG+1 ($4.19)
MP1 ($6.47)
MP2 ($5.98)
MP3 ($10.35)

Preflop: Hero is BB with Q, Q.
UTG raises to $0.1, 1 fold, MP1 calls $0.10, MP2 calls $0.10, MP3 calls $0.10, 1 fold, Button calls $0.10, 1 fold, Hero raises to $1.4, UTG folds, MP1 calls $1.30, MP2 calls $1.30, MP3 folds, Button folds.

Flop: ($4.52) K, J, 2 (3 players)
Hero bets $3, MP1 calls $3, MP2 folds.

Turn: ($10.52) 7 (2 players)
Hero bets $2.07, MP1 calls $2.07 (All-In).

River: ($0) 6 (2 players, 1 all-in)

Final Pot: $12.59

So go for it. I know very little about bet sizing. This is my biggest weakness. Pre-flop I'd rather just take it down right there OOP, but I got action. Didn't like the king, but felt I should keep my lead. When I wasn't raised I thought I could very well be good here. Is this bad thinking?

EDIT: The $2.07 bet is because that's all he had in front of him.

Do you have any reads on villian?

Bet sizing - Post flop, your bet sizing is good, roughly 2/3rds of the pot, but pre-flop is a bit large. A standard pre-flop raise would be 3x big blind + 1 big blind for each limper - or roughly pot sized. I would have made the pre-flop raise to about $0.70 - if someone is going to fold to your raise, they would also fold to a raise of about $0.70, so anything more is a bit of a waste and only likely to be called by something that beats you.

As played, I would probably check / fold the turn. If your pre flop raise had been smaller, your bet on the flop would have been smaller and therefore you'd be less pot-committed and find a fold easier. The flat call on the flop is quite a give away that he has something strong.

Unfortunately, a flat call in micro stakes doesn't mean your queens are good - I have seen people with a set / straights / flushes check all the way down to showdown - it is possible that villian is just passive or a donkey. After he flat called the min raise pre flop, then flat called your huge raise, I'd put him on high face cards (likely including a king - quite possibly KJ) or a medium to large pair (Jacks?).

If he called your pre flop range with donkey cards and lucked out (K7, etc), note his name and look to play with him in the future, as he will give you all his money in the long run.

Preflop is a little large. Standard is 4 x the bb plus one for every limper... plus I bump it up an extra BB at super low stakes since the majority of the field overcalls their hands. So, with the minraise and 3 callers, making it $1 to go sounds good.

Don't feel obligated to c-bet. Chances are one of these numbnuts has K-10 or something silly a good portion of the time, and is not letting go. They only know what a kicker is when they get to showdown and go... ooooh... right, kickers matter. Also you can tone down the size of the bet if you choose to... it really won't hurt you against these guys.

You're committed to this pot by the turn, but I don't like betting out. If the rest of the $ is going in, let your opponent do it.

You stated: When I wasn't raised I thought I could very well be good here. Is this bad thinking?

What do you think your opponent could be holding that you are ahead of here. The only real posibility I can think of is A/J. I think if the villain had a smaller pocket pair he would be scared to call thinking you either had AK or a big pair and in either case villain would be beaten. I thinking leading the flop is find, but once you are called you want to get to showdown as cheap as possible.