T3 and T1 at FCO are terms that may soon disappear from usage. T3 actually describes, gross modo, everything except the T1 terminal in terms of handling. The actual building where the plane docks (or the "vast area" where planes often stop) is in a way independent of the terminal. AZ passengers (European flights) and airlines that are linked to it (e.g. Sky team minus Delta) are handled at T1, everything else at T3. Easy jet flights are handled at T3, but where the plane is physically can differ. To make matters a little more complicated, once airside, T3 and T1 designations disappear, and all arrival and departure gates (and areas) are designated by letters... You'll notice that I did not mention T2 and T5, let's forget tham in this context.

At any rate, if bussed, this will add another 10-15 minutes net to your arrival but there's no way of knowing. be that as it may, luggage retrieval for you will be in the basement of T3, downstairs from the check-in area of Emirates.

I repeat, though. this is a very risky connection, especially with your 1 year old kid!