Welcome to BYH and congrats on the quads. (I think)

That is a lot of kids for a boer to raise and I would certainly be thinking about supplementing with a bottle. If you are raising them for fast growth most people would just flat out pull two of them and bottle raise them. If you are just raising them "for fun" and quick growth isn't an issue you can certainly let the dam try, but not sure that she can do it. If you need to supplement you can just use whole cow's milk from the grocery store.
About the CDT shots. You can give the dam one now but it won't help the kids.
Kids born to does with uncertain vaccination history or with questionable colostrum ingestion within the first 24 hours of birth should be vaccinated at 7 to 21 days of age and then given a booster three to four weeks later. Alternately, tetanus antitoxin (150 - 250 units) can be given at birth or at castration.
The weak legs can be just the fact that there are multiple kids but I would suspect a selenium deficiency and ask a vet about getting some BoSe for the kids and dam. I live in a Selenium deficient area and we give it to all the does 1 month before kidding. The BoSe has the vitamin E in it as well. You can also get a Vit E selenium gel but I have never used it.
http://articles.extension.org/pages/27116/goat-vaccination-program