Danidean14 - get a separate passport for your son. You'll have to pay the same Fiancee Visa fee for him as you do for yourself and he'll get his own pretty sticker in his passport. After you get here and get married, you then apply for the FLR (good for 2 years) on both your behalfs, and he'll get a stamp in his passport as well. Works out well for you that he's so young, because he'll still be young enough for you to apply for citizenship for him after the requisite time (which used to be 3 years through marriage, but I'm not sure if they've changed that or not). Then he'll have both a US and a UK passport and shouldn't have any trouble going back and forth once he's older.
Don't remember exactly your custody situation, but please be aware that you'll need the father's signature to get both the passport AND the Visa. Unless you're the only name on the birth certificate (as in my case). Otherwise, make sure you've got your ducks in a row on that.
Good luck!