Acoustic pros: Makes more noise easier. Probably a bit more "girlish" and less lesbian-rocker than an electric. Cheap, easy to tune, easy to change strings on. Tons of easy songs to learn so she won't lose interest quickly.
Acoustic cons: Easier to break, because kids break things. Louder than an electric when practicing, so you'll hear it all the time (that's why they call it "acoustic" after all..). String changes can be a pain in the ass with inexpensive ones, because the bridge pins wear out quickly.
Electric pros: Easier to play than an acoustic, better for small hands. Can take more abuse. Still easy to change strings on, probably a little easier than an acoustic. Practice is quiet, so you won't hear her unless she's plugged into the amp. Can use thinner (lighter gauge) strings, which are also easier to play and easy on small hands. Easier to play chords on.
Electric cons: When plugged in, you'll hear it, and probably drive you nuts. Requires a bit more maintenance than an acoustic to keep it playing well. Lighter strings break easier and more often.
As long as you don't mind doing the odd string change for her when she's starting out, it's really a coin toss. If you think she'll stay with it, get her an acoustic. It'll build better fundamentals and hand strength. If you just want to get her started on the cheap with something that makes noise to see if she'll like it, IMO go for an electric.
A bunch of brands make 3/4 scale / mini sized guitars for kids. Something like this is only $100 and just fine for an eight year old:
Electric:
Amazon.com : Squier by Fender Limited Edition Mini Strat Electric Guitar Bundle with Strap, Tuner, Picks, and Polishing Cloth - Blue : Electric Guitar Packages : Musical Instruments
Acoustic:
Amazon.com: Oscar Schmidt OG1 3/4-Size Acoustic Guitar - Natural: Musical Instruments
They're both going to be shitty, but if they end up being dust collectors, you're only out $100. (Plus another ~100 for the amp on the electric side.) If she ends up still playing a year from now, get her something a bit nicer. I've given lessons to a ton of kids over the years, and the ones that stick with it and really enjoy it tend to take pretty good care of their instruments. (Kids who don't give a shit, on the other hand, don't.)