To give you a better answer we would really need to know everyones stack sizes, if it's a very short stacked table, a shove might give you some fold-equity, but if the table all have bigger stacks, something like 15+ bbs, then it's not worth even worrying about. But if you have no fold-equity why do you call? I don't think you're understanding what the concept of fold-equity is for, or rather how to apply it.
To put it bluntly, you have 4.5 big blinds, and you have QQ, put your chips in the middle. Calling here is a big mistake. Even if they all call, you have a top premium hand, what are you waiting for with 4.5 bigs? This is pretty much as good as it'll get for your tournament life.
When action gets to you there is 7.5 bb in the pot, you're likely going to be called by shoving, but perhaps the players at the table are bad and only hear the all-in and aren't paying attention to the chips so you get folds. Even still shove pre-flop, big mistake calling, you don't have a stack to call.
In this situation don't worry about fold-equity, you're already crippled and you're goal should be to get it in with a good hand and hope to double or triple up. Would you rather stick 4.5 bbs in with a top hand for the chance to minimum win 7.5 bbs or would you rather call, fold and then stick your last 1.5bb with any random hand for a chance to only win 1.5bb minimum?