If your details are correct:
7 limpers x .25 + 1.00 raise + .75 = $3.50 in pot.
You bet $1.25

He needs to call $1.25 to win $4.75
Pot odds to him are 3.8 to 1
Considering implied odds, he is somewhat justified to call and chase his gutshot str8 - even if he thinks he can only win with a str8 (in reality he would consider the possibility that a K might win it or you are bluffing; then he really has odds to call). You probably want to bet more on the flop, especially having been the one who raised pf.
Very unlucky that the Q came. No way to get away from it at that point.

When he just called the flop and did not raise it I would assume he caught some of the flop but not the Ace. If he paired an ace he should have raised. But he only called so you have to wonder what he's hanging around with. 2nd pair - Jacks or pocket mid-pair - or a str8 draw are about the only possibilies that make sense. Pot is about $3.50 so your bet was a bit low at $1.25 giving almost 4:1 (with implied odds that is enough to see at least one more card) - bet at least half the pot and if a flush draw is also present go to 2/3 to pot size.

Turn - nice card but makes a str8 more plausable. With you holding a pocket pair of Queens, the str8 was less likely but there it is! Once he re-raised you you had to wonder but I can't see laying this down. My guess is if you hadn't gone all-in, he was going to do it for ya the next round. Your only hope is for the board to pair up for the full house and that would be 9 outs - 10 counting the case Queen!

You have proven that trips will lose up to 20% of the time - that's poker! About the only 'error' might be betting too little on the flop and making it more difficult for your villian to draw to an inside str8 - although he was drawing at 10.5:1 as far as he knew and 22.5:1 in reality since you had the pocket queens. He made a mistake by calling and unfortunate for you got rewarded for it!