Indeed, should not be possible:
http://www.changiairport.com/in-tran...it-information

Tiger does have the TigerConnect option, but I think that's only supposed to be for connections between Tiger Air flights. However, point is moot given the lack of late-night flights.

Clearing Singapore immigration and customs normally does not take too long; however, it will still be tight given you only have 1:30, and you will have to go to a different terminal to boot, T3 --> T1 - tack on ~5-10mins for this. Plus, Qatar deplanes on the other side of T3 from the T1 Skytrain, so you can't just hop directly on.

It can be doable... you land bang on time (or early), take ~5min to taxi, are first out the door, 3-5min to immigration, clear in <5min, get to the Skytrain and then across to T1 in 10min total, get and a couple more to walk through the departure hall and find AirAsia's check-in desk for verification.

If you think you think it is worth it to chance it, go for it. However, if it were me, I'd either buy a MH ticket to get to KUL by 10:30-ish (buy a RT with a throw-away return leg, much cheaper right now) or get a seat on the later AirAsia flight.