KQs is strong enough to push. You usually do not want to push as wide of a range for 12 bb as you would for 10 bb or 8 bb, since the reward of stealing the blinds is smaller in comparison with the stack you risk. On the other hand, your opponents are not getting as good odds when you push, and they should respect your range a bit more.
You definitely don't want to take a coin flip here, but the true disasters are only when you get called by QQ+, AQ, or AK. KQs has 44% equity against AJo. When you hold KQ, there are only 36 combinations of QQ+ AQ+ out of 1225, or about 3%. With 3 players acting after you, the chance that you are crushed is only about 3x3% = 9%, and you still win some of the time when you get called. This is an acceptable risk compared with the 300 chip reward from stealing the blinds. So, pushing should be better than folding, and in fact you might be able to push some weaker hands, too.
That leaves the question of whether you can do better by making a small raise than by pushing. I favor pushing against better opponents, but some players will only resteal with good hands against which you have an easy fold, so an argument can be made for trying a small raise to 2-2.5 bb. My default play is to push.