here's the time table for some fligths from kl to tawau:
Airasia Sdn Bhd
AK 320 Kuala Lum Intl. (KUL), Kuala Lumpur, Malaysia 09:50
Tawau (TWU), Tawau, Malaysia 12:35
Non-stop
733 2h45min Daily
Malaysia Airlines
MH 2662 Kuala Lum Intl. (KUL), Kuala Lumpur, Malaysia 12:45
Tawau (TWU), Tawau, Malaysia 16:50
1 stop(s)
734 4h05min Daily 1 stop (kota kinabalu)
there are other combinations with a stopover in KK usually. unless you have to depart KL after 1230p there is no need to overnight in KK.
i use the following site when i need to know both availability and timetable of flights:
www.amadeus.net
it does not provide pricing though, but i have found it to be very useful over time to plan complex itins.
/paul