Should I be shoving this turn in a RR pot? [nl10]

[larry31]

Hey, I played this hand earlier in which I check folded the turn but I have been thinking about it alot and think the best play would have been to push.

What do you think?

The villain has only played 5 hands at the table so no reads

Poker Stars, $0.05/$0.10 NL Hold'em Cash Game, 5 Players
LeggoPoker Hand History Converter

BB: $15.55
UTG: $8.50
CO: $10.35
BTN: $10.10
Hero (SB): $10.15

Pre-Flop: A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/spade.gif[/img] dealt to Hero (SB)
2 folds, <font color="red">BTN raises to $0.30</font>, <font color="red">Hero raises to $1.10</font>, BB folds, BTN calls $0.80

Flop: ($2.30) 5[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/heart.gif[/img] (2 Players)
<font color="red">Hero bets $1.60</font>, BTN calls $1.60

Turn: ($5.50) 8[img]/images/graemlins/heart.gif[/img] (2 Players)

I did a quick equity calculation on what i thought his range of hands might be, it might be abit loose? But I find at this level my 3bets don't get to much respect.

Board: 5h Tc Qh 8h
Dead:

equity win tie pots won pots tied
Hand 0: 43.799% 39.34% 04.46% 1402 159.00 { AhKs }
Hand 1: 56.201% 51.74% 04.46% 1844 159.00 { 55+, AJs+, KQs, AJo+, KQo }