Yes, you will be able to drive in Singapore, all you will need is your driving license. Singapore and Malaysia both drive on the left so you should have no problem at all, you won't even need an International Driving Permit, as both countries are members of ASEAN.
If you are staying longer than a year, you would be required to obtain a Singapore license so bear that in mind if that is the case.
The Land Transport Authority in Singapore has brought in an Electronic Road Pricing scheme to ease traffic congestion but this only applies to peak times on certain roads. Basically an electronic gantry is placed over the road at certain locations and all cars have to be equipped with an In-Vehicle Unit , a rectangular shaped device which is stuck on the inside (bottom right) of the windscreen , and deducts the toll price from a cash card. The cash card has to be inserted into the device by law. There is no charge for entering the area during non-peak times.