Ask if they are milking now, how often (once or twice a day.) I'd ask about the baby....it is amazing how many people think you can wean a goat as soon as they are eating hay. And how many think you can switch from mama to a bottle late in the game. Ask me how I know....boy, was it traumatic when I bought Ginger at five weeks old.
Ask to see her get milked and try it yourself. What if she is a raging b*%$%#? You wanna know.
How old is she? (There are age/teeth charts online, but they only are useful for goats under 3, I think. If they say 3, well, take it with a grain of salt.)
Does she have horns? Observe her behavior with the other animals. I went to look at Ginger's mom, a doe in milk, and came home with Ginger instead. I did NOT like the way Ginger's mom used her horns with no warning and viciously. Not sure where Ginger got her personality, but I see a tiny bit of Grandma in Ginger's baby, Peach....but her horns go back, not sideways, so she is not as bad. So take your time and dress warmly and watch from a distance. For a while.
BTW, Mya has HUGE horns but is very fair in her use of them. Everyone sees her coming and she does a straight ramming bash, no hooking at eyes or bellies. I'm not saying horns are bad, if you don't mind them.
Ask if she's been tested and if you can have purchase contingent on clean bloodwork. They may say nevermind. Or you need to decide if it is important to you. I'd say less so if you are not interested in keeping goats once the cow is lactating.
Take a look at her feet. Have they been trimmed? Ever? Oh, you have sheep, you know this!
That's all I can think of right now!