I'd have some concerns about doing such a long rail journey with a toddler - but on the other hand people go on long flights with toddlers, and there is more space on a train than inside an aircraft, so it may not be so bad.

The Italian part of your itinerary sounds a bit rushed. If you just want to "do a quick Rome sight-seeing" then you seem to be travelling a long way for very little. I'd say either cut Rome out of the itinerary (which would shorten the rail journey by a few hours), or spend more time there and cut out something else.