The following applies to cash games.
M33K3R's advice is very good, AJ is way better from position than out of position (every hand is, but AJ more so).
You've got a strong ace, if you take the flop heads up you're ahead most of the time. Better still, when you do hit there are a lot of hands that will pay you off. Hit the J and there's a whole range of J's that will pay you off, hit the A and even more hands will pay you off (since Ace-rag suited is very playable). The reason however that it gets most of it's value from position is that there are a lot of hands that have you dominated and you need position to figure out if you're up against one of them.
I fold AJ from early position very often when facing a raise (doesn't have to be a big raise either), I suggest you do too.
When someone leads out before you, you've got to ask yourself if they've got AK, AQ or big pockets.
KQ really shouldn't be the hand that causes you troubles, AK or AQ are going to be the thorn in your side when you play AJ.
If you're having trouble against KQ, I suspect what you're doing is over valuing your AJ and not wanting to throw it away when you miss. What you should be doing is:
1) Looking for A flops, here you're often ahead and likely to get some money out of AT and Ax suited. Keep in mind that even when you hit your A, it's often correct to fold because you can be up against AK, AQ, big pockets or someone has flopped two pair or better.
2) Looking for jack high flops, here you're ahead of everything but big pockets and two pair or better, you're going to get paid off by KJ, QJ, JT and anytime someone overplays something. These flops are where AJ makes it's money. I'm not saying don't fold here, it's still correct to fold sometimes and you should be on the lookout for bigger hands, but it will be rare that you're beat at this stage.
3) Betting your ace high, a lot of the time it will be good on the flop if you take it heads up and you should bet it because it can be outdrawn very easily. Of course, this is highly dependent on your read in the particular hand and you will end up check-folding or bet-folding sometimes.