While I agree with how you played the hand, I think your thinking on the turn is flawed
while it's true the Q didn't help your hand, it helped your range
because you have a lot more Qx hands than TT-JJ that were hurt by this card

your hand went down from 27% equity to 22% equity vs. a 9 so it's not like that card was terrible for your hand either, since it gave you additional outs

consider sometimes betting that card