according to the strategy you played correctly, but its always good to annalyze the situation.
The flop is paired, so its not very likely that he got a piece of it, however, he can hold overpair, but likely overcards or lower pockets. Besides, his overbet looks quite weak imo. i would put him on AJ-AQ or smthing. If you have any reads that your opponent is playing overagressively postflop, then you may consider push.
Pot size: 12BB
Stack size: 11BB
If you push after his bet and he calls, you are getting 2.1:1 pot odds, which means that you need to win in 1/3.1 = 32% of the time.
Lets consider he is moderately loose opponent with a calling range from SB:
22-88, AQs-A6s, K9s+, AQo-A8o, K9o+
Against this range we will win 58% of the time, which is more then 32%) I guess we will get more than 32% equity nearly against any possible realistic range... So mathematically correct play here is push.
But in the beginning its better to stick with basic strategy and fold, before you will be able to recognize situations where push is profitable... so well played)
You should push if he checked or you are first to act, since your stack:pot ratio is 1:1.