Flopped underfull, correct turn all-in?

[luckycharms]

I put him on a high queen, and was right. I think my pf and flop play was just fine. Should I wait til the river to see what it brings? I'll almost surely be able to get a call there, and I can play it safe, tho the only river I'd really lay down to would be a 2 or Q. Thoughts?

PokerStars No-Limit Hold'em, $0.50 BB (9 handed) converter

saw flop|<font color="#C00000">saw showdown</font>

MP2 ($19.85)
<font color="#C00000">Hero ($48.50)</font>
CO ($50)
<font color="#C00000">Button ($51.25)</font>
SB ($48.40)
BB ($61.45)
UTG ($62.50)
UTG+1 ($51.75)
MP1 ($29.20)

Preflop: Hero is MP3 with 4[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/spade.gif[/img].
UTG calls $0.50, <font color="#666666">2 folds</font>, MP2 calls $0.50, Hero calls $0.50, <font color="#666666">1 fold</font>, <font color="#CC3333">Button raises to $2</font>, <font color="#666666">2 folds</font>, UTG calls $1.50, MP2 folds, Hero calls $1.50.

Flop: ($7.25) Q[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
UTG checks, Hero checks, <font color="#CC3333">Button bets $2</font>, UTG folds, <font color="#CC3333">Hero raises to $5</font>, Button calls $3.

Turn: ($17.25) 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $9.5</font>, <font color="#CC3333">Button raises to $19</font>, <font color="#CC3333">Hero raises to $31</font>, <font color="#CC3333">Button raises to $44.25</font>, Hero calls $10.50 (All-In).

River: ($103) 2[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

Final Pot: $103

Results in white below: <font color="#FFFFFF">
Hero has 4h 4s (full house, fours full of queens).
Button has As Qc (full house, queens full of twos).
Outcome: Button wins $103. </font>