Are you flying on a normal or full fare ticket and flying with Jetstar Asia (3K)? If so then after landing at T1, make your way to Transfer Lounge C near Gate C1, which is well sign posted. Then to check in for your Jetstar flight, At the transfer lounge counter, show the staff your old boarding passes, Passport, onward flight Itinerary or Booking reference (preferred paper copy) & luggage tags for them to arrange your luggage transfer from your Jetstar flight. You can remain airside and do not need to pass through immigration.
The transfer staff are very friendly and helpful normal takes a few minutes. However if this is separate tickets then you will bear the risk if your miss the connecting flight. You will be classed as a no show and need to buy another ticket - which could be expensive at the last minute.
If you travel on the ID or staff travel ticket then you will have to collect your luggage at SIN - clear customs go upstairs and then check in again at T1 departures landslide counter, (3K counter closes 45 minutes before flight departure) before going back through security and immigration then your onward flight to Malaysia.