We stayed here with our 22 months old baby.
The location is amazing!!!!! Trastevere is a great location for night time and is also very pretty during the day. It is walking distance to everything (if you don't mind 20-30 minute walks which we didn't), or you can take one of the many trams/buses around.
The kitchen is small but has everything you need (apart from an oven if you really must have one. We were fine with the microwave and stove top).
Francesca is very responsive to texts and will help with anything you need ASAP.
We had no issues while we were there - wifi and everything else worked fine which I always find as a bonus.
There are some stairs in the apartment (about 3) which he is fine with, but if you come with a child you might want to be aware of.
The advantage of all the restaurants around is that you can either go out or take out and eat at home. It is all so close and it is where everyone goes anyway.
I would recommend staying there. Simple apartment yet located perfectly with a very nice host.