This depends on whether your partner has a solid early reentry, whether you have a good entry, and what your signalling conventions are.
You are confident that your partner started with KQTxx, and thus declarer holds Axx of this suit.
Above all you want partner to continue this suit. discarding the jack might do that, depending on your agreements, but another possibility is to play your most encouraging card that is not the jack. If partner leads low to your jack, you can play your jack. If declarer wins with the Ace, declarer will have no stop left in the suit, and if either of you get in, you will get your four tricks in this suit, plus one entry trick, setting the contract by at least one. If you discard the jack and partner continues high, much the same result occurs.
However, if there is any chance that your partner holds the KQ9xx you must get partner to lead low to you jack on the second trick. if you discard the jack, declarer will make both Ace and the Ten, a possibly vital trick for declarer.
With a 4-card suit there is no need to worry about immediate unblocking as long as you don't hold the jack until the 4th round. They key issue is to signal partner to continue, either with an honor or a low card. If partner continues the suit, and either s/he or you have a prompt re-entry, your side is assured of four tricks in the suit. Once declarer wins the Ace, whichever member of your side gets back in first can continue the suit, and your partner's remaining cards in the suit should run. As long as declarer cannot collect nine winners before letting your side back in, the contract should go down.
If you play a low card at trick 1, and partner continues with a low card in the suit, play the jack at trick 2 and continue the suit if it is allowed to hold. If partner plays the king at trick 2, drop the jack on it (if yu didn't play it at trick 1).
What would your partner lead from KQ9xx? Why does your partner lead the Queen from KQTxx anyway? the standard lead here is the King, I believe.