Hi,
You need to set a budget for this trip (this is most imp).
Then, fix how many days you wish to spend out of Qatar.

All tour operators suggest tourists 3/4 days at Singapore, but my personal suggestion - you must spend minimum 8 days in Singapore to experience this city.
Hotels per night start from 60SGD.
During my backpacking days I even stayed in cheap youth-hotels for just 20SGD a night :D

Every hotel has tip-up with Singapore Tourism Board (STB) for all the sight-seeing packages and every hotel sell those packages as well as has pick up & drop off facility. As soon as you land at the airport, buy 'EZ-Link card' thru the vending machines by putting cash in, This card is one thing, without which your Life could be in mess there, it covers almost 5 public transport operators (saves you fm many hassles while commuting), just board any MRT or bus as & when you feel like.

From here, you may travel to Vietnam (3 days) and to Cambodia (3 days), Malaysia requires minimum 5 days.

If you need any further info, I am reachable on 6989 650.
Yogesh Pagar