The new Hilton is located at Sentral which is a 28 min train ride from KLIA. The Hilton website indicates that this hotel will open its doors in July 2004. Since the external facade of the building and the landscaping appeared to be completed a couple of months ago, it may well open its doors a little earlier but I dont think there will be a January 2004 opening date.
Taxis are relatively inexpensive in KL and since you are travelling with a baby it may not be a good idea to go around town using the trains. Also bear in mind the heat and humidity in this region before venturing out under the sun with your baby.
Hope you will enjoy your stay in KL.