With just 5BB to start the hand, poker is really simple. Only move is all in or fold preflop, and QQ is of course always going to be all-in. Only exception is, if its a satellite, and you can fold your way to a sure ticket. Same idea with a DON (dubble or nothing).
For me this is not a bad beats but just bad luck any bigger pair can lose to a smaller pair in an allin
There is no scientific definition of a bad beat, but to me having 80% equity and losing does feel like a kind of bad beat. It will happen of course, but it still suck, when it does. If we get down to something like 60/40, as when we have AJ against KQ, then I no longer consider it a bad beat.
Not much to say about this hand. You have 5 BB with the blinds coming up in the next hand and you have queens. You shoved as you should have and got unlucky. You want hands like that to call and roughly 1 out of 5 times lower pairs beat higher pairs. No one likes it but it is part of the game.