she really looks small. size of newborn kids is determined by genetics. to answer your question, if she is this small and you breed her, there could be problems when she get her kids.
why do you want to support a breeder with obviously not so good management? besides, i had quads and triplets, never had a stunted kid between them, maybe one that started a bit slower but after a couple of weeks, no difference. it really is all management. my goats all have a sweet temperament too and a lot of breeder have super sweet animals that are better cared off and would give you a better start.
you said, you can only afford $125 for a doe. now i'm wondering if you can afford to feed such a little one that will never give you your investment back? would be the same if you through the money out the window.
if you would just add a little bit, you might be able to get a nubian that will be healthy and productive and a source for family milk.
just food for thoughts
the genetic default you are talking about is G6S. you can have your doe tested(probably should) before breeding her.
i would also test for cae,cl and johnes just to be on the save side.