My husband is Argentinian and although we have lived in England for the last few years we have travelled a lot in Argentina, and lived there. That said, nowadays we tend just to rent a house near my husband's family and stay put rather than travel around. Before children, though, we spent a year travelling all over the country and it is a fantastic place - just make sure you go for a long time so you can see a fair amount of it.
You can definitely buy everything you need for children and, yes, kids are welcome everywhere. Travel everywhere is done on buses and the distances are huge so I have to say I wouldn't fancy doing that with a child. All the buses have at least reclining seats and many have seats that are more like beds so I suppose it could be possible, depending on your child. I certainly wouldn't want to be a passenger on a long bus journey with my kids! If you are going for a long time you can look into buying a car (which is what we did) but the bureaucracy makes it all a bit of a nightmare. Otherwise hiring a car is easy. We always hire at the airport - it is expensive though. You could also look into flying to Chile, hiring a car there (it's cheaper) and then crossing to Argentina (great trip which puts you right in one of the most beautiful parts of the country). I never really came across a train - there are very few and they don't go anywhere particularly useful.
I don't have much experience of staying in hotels as we took a tent with us and camped everywhere. Every town, village, national park has at least one campsite and you can also camp pretty much anywhere you like if you want. December, January and February are the months when the whole country is on holiday so everything does get crowded, particularly as everyone camps. Also, Argentinians stay up very late, as do their children, so be prepared to find it difficult to put your daughter to bed at an English-type time.
I assume your daughter will be eating pretty much normal food. Argentinian food is very bland and we have never had a problem with getting our son to eat it. There's lots of pasta, lots of things made of pastry, lots of cheese, chicken, salad and then stacks and stacks of beef. If your daughter is not a beef eater, don't worry, there is always an alternative. Depending on where you are, lots of fish too. You can drink tap water everywhere.
Argentina used to be very expensive but the recent crisis has made it much much cheaper.
Depending on what kind of holiday you're after, how long you're going for and how much you are prepared to spend, I think Argentina is a fantastic place to go. I really do think you need time, though, and a car.
If you want to know anything else, do ask. You can also ask for my email if you want to know more about good places to go etc.
Hope that helps.
One last thought - fly direct. If you're in Britain go British Airways if you possibly can. It's more expensive but we went with Alitalia via Milan in December and it was a nightmare - much longer and not nearly so child friendly - eg only one bassinet on a plane with dozens of babies, all of which had pre-booked bassinets. Horrendous.