My daughter, a daily iPad user from about 9 months old (now 2.5!) exclusively uses it in a landscape orientation and I've never seen her try otherwise. That said, I'm the same unless one handed operation is desirable (no dirty thoughts, friends!)
Interesting. I use my tablet landscape except if I'm reading an ebook. Maybe there's something more natural about landscape views, and I've been conditioned to read in portrait by printed material.
On smaller devices I find portrait more natural, possibly due to the one-handed nature of use.
Out of interest: do any of the apps she uses support landscape? Is she choosing that orientation or are the app designers making the decision?
Most of the apps are landscape or are better in landscape (e.g. YouTube) so the decision may not be as natural as it seems at first glance.
Another thing to consider, though, is that a high proportion of books for under 3s are in landscape too (in my experience at least). So maybe the book industry has also had this question crop up over the years too.. :-)