In terms of high card hands in this spot, which hands would you bet on the turn?
The Q is a good barreling card, but if you here also bet T9s, J9s, JT, KJ, A4s, A5s,..., AT, ..., etc, then you are bluffing too much. You also have no outs really, and the pot isn't huge. What's the plan for the river? Barrel again? If so, then there is a risk that you bluff too much.
On the other hand, you are close to the bottom of your range. but maybe not close enough, since there are the 2-card gutshot straight draws to bluff, i.e. T9s, J9s, JTs. That's 12 combos, almost enough to balance the the probably about 50-70 combos you should bet for as value on this board. (I like to check with a few value hands to check-raise or check-call.) If you don't play T9s or J9s, then KTs is a logical hand to bluff with.
Suppose you c-bet 100% on the flop here (wong!!!) and have T9s, J9s, JTs in your range, and suppose you bet 99+ for value. Then, bluffing with T9s, J9s, JTs and KTs makes you perfectly one-street balanced. But, there is a better choice! Bluff with two KTs and two KJs, i.e. the ones that have flush draws.
It is probably good to bluff a little more than 1-street balancing indicates (stacking bluffs). So, all KTs should then be bluffed.
Besides balancing:
MP3 is a fish that took two cold preflop. If he is a 40/4 type of standard fish, then you should know that his range is composed of a shitload of high cards, pocket pairs, and above all, Ax. Many high card combos hit that Q, the pocket pairs aren't folding. More importantly, a fish doesn't play A5o in order to fold it on the turn on a board like this.
So, my answer is "yes, ", this may a barreling hand, but then be careful not to barrel every goddamned Kx and Ax that have missed. (One has to face the fact that we missed this board completely. There are times to give up.) Also, consider the range of the fish.
Below is a suggestion of a 1-street balanced range for the turn:
Combonator Output combonator.com
Board: 2
3
8
Q 
Entire range: 168
Grouped: 168 combos 100.0%
Ungrouped: 0 combos 0.0%
Group 1: 72 combos 42.9% (42.9% total)
Group 2: 16 combos 9.5% ( 9.5% total)
Group 3: 80 combos 47.6% (47.6% total)
Group 1: Value
88+, AQs, A8s, AQo, KQs, KQo, QTs+, 98s
Group 2: Bluff
KJs (2), KTs (2), J9s+, T9s
Group 3: Check
77-66, AKs, AJs-A9s, AKo, AJo-ATo, KJs (2), KTs (2), KJo