top two problem

This was one of my very first hands on this table.
I have a hard time playing hands like these. After his last raise I knew I was probably beat but I was so commited. How should play these? I feel it's weak to fold to his initial donkraise altho a minraise usually screams strength. I don't like just calling either because he might be on a heart draw? I know I screwed this up bigtime but any help on how to play these appreciated.

Party Poker No-Limit Hold'em, $ BB (10 handed) FTR converter on zerodivide.cx

UTG+1 ($63.55)
UTG+2 ($62.30)
MP1 ($103.25)
MP2 ($50)
MP3 ($49.25)
CO ($68.39)
Button ($47.25)
Hero ($49.50)
BB ($57.85)
UTG ($172.89)

Preflop: Hero is SB with A[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/spade.gif[/img]. Hero posts a blind of $0.25.
<font color="#CC3333">UTG raises to $1</font>, UTG+1 calls $1, <font color="#666666">1 fold</font>, MP1 calls $1, <font color="#666666">4 folds</font>, Hero (poster) calls $0.75, <font color="#666666">1 fold</font>.

Flop: ($4.50) T[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">Hero bets $4</font>, <font color="#CC3333">UTG raises to $8</font>, UTG+1 folds, MP1 folds, <font color="#CC3333">Hero raises to $20</font>, <font color="#CC3333">UTG raises to $32</font>, Hero calls $28.50 (All-In), UTG calls $16.50.

Turn: ($101.50) T[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

River: ($101.50) 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

Final Pot: $101.50

Results in white below: <font color="#FFFFFF">
Hero has Ah Qs (two pair, aces and queens).
UTG has Jd Kd (straight, ace high).
Outcome: UTG wins $101.50. </font>

[yvesaint]

its not really feasible hes on a heart draw considering you hold the Ah

call the min-raise, lead turn ....if he raises big consider dumping it, especially to that nasty turn