You can travel to Singapore from Kuala Lumpur by bus, rail or air. It will take approximately 4-6 hours drive, 8-9 hours by train and 1 hr 15 mins by air.
The budget airlines sector has bring down the fare quite a bit, below are some budget airlines that ply the Kuala Lumpur - Singapore route:
1) Firefly (operates from Subang Airport) is a subsidiary of Malaysian Airlines, the advantage is definitely the Subang Airport being nearer to the city than KLIA (Kuala Lumpur International Airport) or LCCT (Low Cost Carrier Terminal) but a recent fare increase and the fact that the treat children above 2 as "adult" is a let down.
2) Tiger Airways (operates from LCCT) and has among the most competitive pricing and check in cut off time is not as strict as Air Asia, prices also go down nearer to departure date. Infant seat belts are available but choice of food on board is not much if you don't pre-book.
3) Air Asia (operates from LCCT) prices ranges from dirt cheap during promotions to "I-can't-believe-they-are-charging-that-price-for-a-budget-carrier", the add-on fees such as counter check in fee are also a nuisance. They are also very strict with check in cut off time (45 mins before departure time)
4) Jetstar (operates from KLIA), the most expensive among the four carriers most of the time, sometimes price is comparable with Air Asia and rock bottom price is only for one way trip with hand carry luggage only. Adding on a checked luggage will cost more than your promotional flight ticket.