Singaporeans entering Malaysia are allowed to stay 30 days or less visa-free in one calendar year. International drivers licence is valid in Malaysia for 1 year only.
All cars are required to pre-register for Vehicle Entry Permit or VEP, processing fee is $10 and it's valid for 5 years. Thereafter, each time you enter or exit Singapore/Malaysia borders it will cost you $20, payment by cash card only as cash payments are subject to an additional $10 surcharge. When entering Malaysia from Singapore, payment is 20 ringgit and payment is by Touch'n'Go cards that are used on Malaysian roads and toll booths. Coming back from Malaysia to Singapore, ordinary cashcards or CEPAS cards are accepted and its $20 singapore dollars.
Some Singapore car insurance covers Malaysia, you might want to extend coverage for all countries before leaving. If your insurance company cannot do that, than you have to buy car insurance at the border, have your car documents ready. If you are driving a foreign car into Singapore, you can only do so for 15 days. Thereafter, you have to apply for an extension from LTA and the maximum is 90 days. If you wish to keep the car in Singapore past the 90 days, you have to apply for COE etc that is the same as a new car purchase.
One last thing to remember is : Singapore registered vehicles at Malaysia borders need to have a minimum of 3/4 tank of petrol. If not you will be turned away at customs or even prosecuted in court and fined up to $500.