There's some not so good advice in here besides the last couple posts talking about not complaining/worrying about bad play, as it is indeed what will make you $$.
I'm going to be a lot less results oriented than most here and go as far as to say you did nothing wrong here. If you wanted to be a little closer to perfect/ideal, the way you described this it sounds like you are out of position, perhaps the SB, but either way I think you should make it 8 or 900 rather than 6. Shoving is fine too, but I really don't see much difference value wise as with just raising 4-4.5x. The times you get called where you wouldn't when you shove/compared to the times you lose because you didn't shove= about the same value imo. If in any doubt or you're just an uncomfortable person, shoving pre is always right and you can';t go wrong.
As played I don't see a hand in their range that can beat you with a free turn card and I don't think there's much wrong with a check, bet, or shove. You checked. On the turn however you need to bet more than 400, you want to bet at least close to half pot, dont check again obv and 400 is a little too small. You can also shove but it doesn't really fit your line of thinking of checking the flop and are hoping someone calls you with a Q or weak ace for that amont. I think they are more likely to call 600 though and then will be priced in for your river all in.
The main point is I don't think there should be as much written about this as I just did. The only mistakes I see are you need to raise a little more pre and bet the turn a little more as played. The other posters advice of shoving pre is fine, but I think it's more based on the result that they make it seem like an absolute. You have aces here. If you have AK it becomes a shove all day. Believe it or not, even on a short stack, you're in good shape with aces and don't gave to shove simply cause you're close to 10BB's. Unless these ppl consistently call shoves, I think there's more value in just raising it because many people like to call/fold, but not call all ins.
I don't like the advice of fold on the river at all though (lol). Think that person may have just been pouring it on. That's my over analysis of a hand that didnt really need to be analyzed for the month
Good luck