Hi, just saw your question and thought I'd weigh in. Note that my view is exactly the same as the other posters, which is to not drive from Singapore to either Kuala Lumpur or Penang but do the flight instead. The difference is that as a long time Singapore resident, I would like to share some anecdotal but factual information about this with you as to why it's not a good idea. In the interest of transparency I don't own a car, however I have gone as far as KL via long distance bus from Singapore and have done this somewhere around 30 to 40 times in the past 10 years.

First is, do you have access to a car in either Singapore or Malaysia? Note that if you rent a Singapore car, often rentals do not allow driving across the Causeway (ie into Malaysia). If you have a Malaysia car even if you can drive into Singapore you will still have to drop it off in Malaysia. As for the drive itself, going to these points can be done on the Federal Highway. Once past Singapore and Malaysian immigration, it would (as Mario33 points out) take four hours to get to KL. Another four hours to Penang sounds about right. On the highway, it's built to a high standard and is like any other limited access toll highway - smooth, straight but monotonous. However note three negatives. First is that all road signs are in the Malaysian language (Bahasa Malaysia); could be problematic if it's an emergency and you can't read the signs. Second is that the long haul drivers use a local signalling conventions for things like passing that after years still don't make sense to me. Finally remember that this is the tropics. If it rains heavily, you might have to deal with driving in monsoon like conditions. Upon arrival in either place you will have to contend with getting to where you want to go - if you get lost, easier if you speak some Bahasa Malaysia, not everyone speaks English. Last but not least, if you rent a Singapore car, you're going to have to go back the way you came; if you rent a Malaysia car in Johor Bahru (southernmost point of Malaysia right next to Singapore), not sure if you can do a one way rental and drop off in Penang.

I'd fly. Look at flying on the low cost carriers - much less aggravating and quite cheap, they do fare sales somewhat regularly albeit the dates tend to be way in advance. You have a choice of Tiger and I think Jetstar, also AirAsia and Firefly (Penang is Firefly's home airport). Look up the threads related to these carriers and the various airports they fly in and out of to get a better handle on these logistics. Good luck and have fun!