Two other ways you can play this are:

1) Reraise preflop and if the other player pushes then you can be pretty sure you're up against AA or KK. This does depend on the other player but early in tourneys you won't have much of a read. I haven't seen that many players willing to come back over the top again with hands other than AA or KK.

This is one of the major reasons you need to pay attention at the table as there are many players who will go all-in with less than QQ so paying attention should help. And if your QQ runs into AA or KK then chalk it up to bad luck for that tourney and move on. Yeah, it's not a 'bad beat' but it is unlucky to have your big hands run into bigger hands. It's rare not to lose any chips on a hand like QQ.

2) You're second option is to lead at the flop instead of going for the check raise. Most of the time you will fold out AK or AQ. If they come back over the top of you on the flop you can be fairly sure your QQ is beat and if they just call it'll be easier to check/fold the turn since you won't have invested as many chips as a check/raise takes.

I generally don't worry about going broke with QQ too much if I'm in a heads up pot with no over cards. It's just too hard to worry about running into AA or KK with the short stacks you play with online and the fast blind structures.