M.R.
I have one of the Sharks, I think it's the deluxe model (not sure, but it was from Bed, Bath & Beyond). I have about 1200 square feet of floor that needs to be swept and mopped, and even with the steam mop, it still takes me 1-2 hours (I tend to sweep it all, them dry swiffer (to remove left over dust, then mop). It takes me a while, but I feel with the steam (vs the old way with a mop with cold water (I used hot water, but it didn't stay hot long enough) mop it at least gets my floors a little cleaner. It did however, take a few mopping session to get a lot of the dirt of the floor (when there's a lot of dirt on the floor, it tends to leave streaks). I am not sure if you can do it holding your baby. When I do it, I usually use both hands in order to get my floors really clean - it's a workout session for me.
I was able to get my boys (21 months apart) to nap at about the same time so I would sweep when they were awake and mop when they were napping. You don't want them to get near the steam (it's hot!).