Depending on her age - even one of the cheap ones with a built in DVD player may be perfect if that's about what she'd be likely to use herself.
@JETURBO Is she more likely to watch the same Peppa Pig DVD (or whatever kids watch these days) or more likely to be wanting to jump on youtube, netflix, facebook etc?
All well and good having the tech to support everything, but if she's not at the age where she has a phone/tablet/laptop a simple, dumb, cheap screen maybe all that's needed. Less than a couple of hundred bucks and lasts a year or so may be fine.
I've always found bedroom TV's for the kids to be great birthday/xmas pressies - every couple of years there's always a decent upgrade option for them that's pretty cheap. As their usage grows, so do the options available for budget prices.