$3 NLHE STT: QQ allin preflop

SB: 1,339 (16.7 bb)
BB: 5,283 (66 bb)
Hero (MP): 2,798 (35 bb)
CO: 2,362 (29.5 bb)
BTN: 1,718 (21.5 bb)

Preflop: Hero is MP with :Qd: :Qh:
Hero raises to 180, 3 folds, BB raises to 400, Hero raises to 1,143, BB raises to 3,519, Hero calls 1,645 and is all-in

Flop: (5,666) :Ac: :As: (2 players, 1 is all-in)
Turn: (5,666) :Js: (2 players, 1 is all-in)
River: (5,666) (2 players, 1 is all-in)

Depending on your read on your opponent, it would be hard to let this hand go preflop.

Reads/HUD numbers are pretty important here. Your opponent 3bet out of the big blind to a very small sizing which looks extremely strong. I'd probably just flat here to keep worse hands in his range in unless you know for sure he will have some 5B bluffs in his range when you 4bet.

4bet sizing should also be smaller, 950-1,000 chips.

Depends on the number of opponents and the position on the table to go all inn with QQ and what kind of turn and if you had many chips I think if you had several chips I go all inn

Since your opening range when 5 handed is wider than in a 9 handed table, his 3 bet range is likely wider too. But as Trent said, the small sizing is suspicious.

If you just call the 3 bet, is there any way you fold on the flop if there is no A or K? Or is it always a shove.