yes, its a good shove, we still have FE to the remaining stacks and we need to get our stack in now being in last place. There is no icm implications here as we have the least chips
You can't really afford to wait for a better hand than QTs on the button because you'll just get blinded/anted down too far.
ICM isn't a factor because you're so much shorter than everyone else at the FT. You have half the chips of the next smallest stack. So think about it this way: you've made it this deep and have already locked up some cash, but you're so far behind the rest of the pack that you really have nothing to lose by getting aggressive and shoving your chips in. And QTs on the button is a great spot to do it.
I don't quite agree that ICM is irrelevant - there is still an ICM factor here but it's not anywhere near enough to stop you shoving here - In terms of mindset you just have to accept that having 11bb you are in high variance territory you can get lucky or unlucky - here you got unlucky - but hoping to outlast bigger stacks when you have only 11 BB would mean you have little chance of getting top 3 where the real money is