QQ better to raise 2.5 bb/call all ins l/a + l/p opps
KK min raise / re-raise/ all in anyone
JJ raise 2bb / call 2-3 bb+. But re raise 4bb+ fold
DON'T. DON'T use a separate bet size for different hands. It is way too exploitable by good players. Use the same bet sizing with every hand, you may just want to differ your sizing from different positions if you feel like it but not based on the strength of your hand. Every open raise you make preflop must represent your whole range, otherwise you are extremely easy to exploit once someone get a semi decent sample size on you.
Especially in tournaments where stacks are generally pretty shallow and preflop play is much much more important than cash games as you get all in preflop very often, you do not want to be giving away information about your hand.
To answer OP, with <15bb stack and a hand as strong as QQ, you can never fold. You just got coolered. In this case it didn't matter since you should never fold QQ with your stack size barring satellite bubbles but next time try to give information about villain's position your position, his table image your table image etc, just as much information as possible. We don't even know if you open shoved, 3b shoved, or 4b shoved, are there limpers what not, although from your post I gather villain open raised(amount?) and you 3b shoved. Otherwise its hard to give feedback.