I would think that a kindle would be a great gift. If you think the Kindle Fire HD is a bit pricey, try the paperwhite. Either way, I don't think she'd be disappointed. I know that's what my niece wants :)
My name is Myka and i am a 13 year old girl. I think a kindle or a nook is a good idea but it depends on the girl. some or more girly than others for me i would want everything on my pinterest so if your daughter has a pinterest look at her "my style" board and see what she has there. I would reallly want some Toms - the shoes - and some music albums such as justin bieber or taylor swift. On My christmas list i put Perfumes. My personal favorite perfumes are the ones from victoria's secret because they smell so goooood!!!!! Bath and body works has good perfumes as well. a Typical 13 year old girls wish list: toms perfumes Itouch Iphone Itunes card a new phone - or if they dont have a phone a cell phone would be a great gift cute earbuds earings and Jewerly in general Makeup Clothes candy - great stocking filler!(:
those are just some of the many things a 13 year old would like.
***REMEMBER***: by the gift for your daughter go off of what she REALLY wants/needs instead of what you want her to want/need.
anyway i hope this helped!!!! and good luck!!!! (: