QQ in SB with a shove and call in front ($3.30)

[Fielmann]

None of the opponents is particularly loose or tight. I'd say small stack has a range of (22+, A6+, KJ+) and big stack has (TT+, AJ+).
Is this a spot to 3bet preflop? I gave it a long thought but couldn't find a 3bet size I liked. Any reasonably big bet would make me committed, which would suck in case A or K flops, while shoving is too likely to chase away hands I beat.

PokerStars No-Limit Hold'em, 3.3 Tournament, 600/1200 Blinds 125 Ante (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

MP2 (t22325)
CO (t154247)
Button (t28782)
Hero (SB) (t54917)
BB (t50681)
UTG (t10071)
UTG+1 (t77685)
MP1 (t17872)

Hero's M: 19.61

Preflop: Hero is SB with Q, Q
UTG bets t9946 (All-In), UTG+1 calls t9946, 4 folds, Hero calls t9346, BB calls t8746

Flop: (t40784) 2, 10, 10 (4 players, 1 all-in)
Hero bets t44846 (All-In)

[baudib]

This is an automatic shove pre, the pot is already 40% of your stack, you're out of position, obviously near the top of your range and facing EP raise/callers. the last thing you want to do is price in the BB.