Busted with AKs preflop. Suggestions?

[Mostly]

I've only been playing for a month, and at this point I think my post-flop play is fairly strong, but my pre-flop play - not so much.

Anyway, here's the situation. I'm early in an online MTT with a little over the average stack with 3700. The blinds are 25/50.

The action is folded to me, I pick up AKs, and raise 3x the blinds. To my surprise, everyone behind me calls to the button, who raises it up to 1200 - double the pot.

I think the reraiser may just be looking to pick up the string, or he might have a made hand or a hand that dominates me, but I'm looking to pick up the pot right there, and thinking that I may stand a decent chance if I'm called, so I push. EVERYONE calls.

The two callers behind me had KK and QQ respectively. The original reraiser on the button had AA which held up.

Besides that hand being a total statistical oddity, do you think I handled it right? My choices at that point I considered to be folding, calling, or going all-in as since that was the only meaningful raise I could make that wouldn't have left me pot-committed anyway. I had just gotten moved to the table so I had absolutely no read on it, other than the fact that the original reraiser was the overwhelming chip leader, which I've found early in a tournament usually means an excessively loose player who's been hitting out. But that wasn't enough to sway my decision. Also, it was still early enough that two callers and a raiser didn't necessarily allow me to put them on a strong hand - the people who will call with anything hadn't been weeded out yet. In my mind I was almost facing three random hands.

Anyway, your advice would be appreciated.

PS: if anyone else had pushed before me, it would have been an easy fold.