Rachel,
Moratalaz is not a bad area. It wasn't considered a very desirable area, YEARS ago, but from all the growing and expanding Madrid has done over the years, it is actually a pretty good place to live, being that its right outside central madrid. (Moratalaz is a suburb, but one of the closer ones, being its right on the edge.)
Its far from the Complutense... the closest thing you'll be next to in Madrid is the area of the Retiro. How long it takes you to get there will also depend on how far into Moratalaz you live, the farther in, the farther away from the center... Transportation is very good, I wouldn't worry about that.
Good luck! You could always look into a Jardin Infantil for your daughter, its like a preschool/day care place, which depending on what you find out before going, it may be an opiton as its not the same as sending her to school.
Good luck!
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Madrid!