You have a couple of choices, either getting a cab from the airport or taking the KLIA Ekspress. I would try the KLIA Ekspress. fare is RM35 (about US$9 each way)

Takes 28 minutes, upon arrival at KL sentral, go the the Putra Train (exit up the escalators, then go through the exit (insert exit card) then walk straight for about 15 meters and turn left through the walkway, past the back of mcdonalds, etc... through the corridor, it opens out, turn left... walk down about 25 meters and turn right to the "Putra" station. It will say the name above the entrance, you can then buy your ticket to "Asia Jaya" or "Taman Jaya" it is about RM1.60 (about US$0.45c). From there it is a 10 minute (no more, no less) walk or cab ride to the hotel. You will need to do the same to get back to KLIA.

1yo baby - I would be more inclined to take a cab from the airport to the hotel. The other alternative is to stay out at the airport (very boring) - but you could then from the airport take a day trip into town. I would suggest with such a short trip to perhaps stay closer to town (JW Marriott, Westin KL - both next to each other, with plenty of shops, plus there is a Putra station about 200m up the road from the Marriott - outside Sungei Wang shopping plaza/Lot 10)