Firstly, the fact that the goat is young - I took on a pygmy female that had been served by her father, and she kidded at just a year old. Its not ideal, but yes, it does happen.
My neighbour, a sheep farmer used to run his female goat (kept for milk for orphan lambs) with his ram, and it did kid x with a ram, although I never saw the kids (or lambs) but he assured me it did.
If you are worried about the goat and ram x, you can take her to the vet, and get her jabbed to stop her becoming in kid, but you need to do it pretty quick.