Depending on what happens with your bags & considering you are traveling in J this can go one of two ways.
1st: Your bag will be labelled to KUL
only, meaning you will have to clear customs & immigration, pick up your bags, check-in again & head back through customs & immigration.
Immigration has a tendency to only staff a number of desks relative to the number of arriving passengers so if you were traveling in Y you'd face a queue pretty much regardless of your arrival time. But since you're traveling in J and assuming TK
also gives it's J passengers some kind of vouchers for the priority lanes you should be able to get through customs & immigration rather quickly. As you've already mentioned, your bags should be available relatively quickly.
Check-in counters for international flights officially close 90 minutes before departure though to be honest that rule does not seem to be set in stone. But your best move would be to check in online which can be done 48hrs in advance, this allows you to drop off your bags at the designated check-in counter up until 60 minutes before departure. That's 30 minutes extra which you might just need if some things are not going your way
If you're in J on MH
you also get the priority lane voucher to get you through customs & immigration quicker but at this point if you've been accepted & are checked in i would say you´ll make your flight. Acceptance at the gate closes 10 minutes before departure.
2nd: Your bag will be labelled to through to PER
. I'm a bit hesitant about this one because i don't think this is currently possible on different itineraries & as you have mentioned already you are arriving on a non-partner airline.
If by some miracle you manage to pull it off head to the transfer desk upon arrival which is located in the satellite terminal where you will be arriving. There you can get checked in & there i would definitely check with them if they have the details of your bags so you can verify they will also make your flight to PER
Expect the first scenario to happen. It's a doable connection & if you arrive on schedule i don't think you'll be under that much pressure to make it to check-in on time.
I believe in coincidences. Coincidences happen every day. But I don't trust coincidences.