I don't think she needs a vet, she seems pretty healthy - but should something happen what do I do?
Here's hoping she settles in well
If you determine she's a hen (for sure) then I'd get some day old chicks and put them in a box and slide the box under her at night. She'll wake up in the morning with her own babies and will probably take over raising them.
I buy Layena Egg Layer Ration for my girls (got rid of my last roo and MAN is it ever quieter without him) and as a special treat and to get them to come, I toss out a handful or 2 of Scratch (Chicken Candy). I holler, "Who wants Chicken Candy?" and they come running. Well, now, they hear the front door open and come running. It's HYSTERICAL to watch chickens run, especially Cochins. I try to do the candy every day at 4 p.m. so it becomes habit and they'll all group up in the same place every day.
I'd keep her in the barn for about a week, then I'd leave the door open and let her figure out how to go outside on her own, if you want to free range her. If you want to keep her in the dog run, get her used to "limo rides" and pick her up and carry her there and then go in and pick her up and carry her back to the barn at night. I had an Ameracauna that would go up on a shelf in the feed barn every night and go to sleep until I'd come by and say, "Ok little sister, it's time for your limo ride." and stick out my hand. She'd step into my hand and then up onto my shoulder for the ride to the coop. They're amazingly easier to "train" (really creatures of habit) and much smarter than you think they ought to be.
Vet for injured/sick chickens. Not real practical because most vets won't know nearly as much as you do about chickens (or at least after you've owned them for a little while) and they tend to either recover on their own, die on their own or if they get bad enough you take pity on them and put them down.
Chickens are addictive and you'll soon become a victim of "Chicken Math". That's kind of an algorithm that goes something like this. 25 chickens plus 12 more from a neighbor plus 6 from the local auction plus 4 from the local feed store plus 2 that you traded with someone for.....and pretty soon you're building a bigger coop. I can't imagine life without my 'girls'!