Yeah, By 7 months age a young doe should be fully switched to hay and grain, she should have plenty of browse(branches, grass, weeds, shrubs, etc. ) and should be eating all on her own.
I would only feed her a cup of grain as over feeding it can cause problems. If she has never eaten it before introduce it slowly.
If you are wondering what brand of grain I would suggest giving her previous owners a call and finding out what they were feeding her before.
Any other info you need? Also, I will direct you to BackYardHerds.com , it is the sister site to this site. Lots of friendly goat people there who would love to give you a hand with your new girl
I would also suggest this site, which has a lot of info on what a goat should and shouldn't eat: