PokerStars No-Limit Hold'em, $0.05 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

BB ($5.80)
UTG ($5.93)
MP ($10.82)
IAGTTAYM ($11.88)
Button ($3.82)
SB ($4.95)

Preflop: IAGTTAYM is CO with Q, Q.
UTG raises to $0.15, 1 fold, IAGTTAYM raises to $0.55, Button raises to $1.55, 2 folds, UTG folds, IAGTTAYM calls $1.

Flop: ($3.32) 6, 5, 3 (2 players)
IAGTTAYM bets $2.3, Button calls $2.27 (All-In).

Turn: ($7.89) 7 (2 players, 1 all-in)

River: ($7.89) 8 (2 players, 1 all-in)

Final Pot: $7.89

Do you think I should shove preflop? Or was my "shove any non ace flop" -line ok? No reads on villian.

With no reads I would push preflop if I wanted the information. But I guess his moves signals aces or kings, right?
Since your hand isn't any worse postflop than it is preflop your allin is motivated... How'd it go?