An 8 week old baby should have had it's second shots and have been wormed. It is still good to give them one more set at 12 weeks and worm again.
As for 'anything contagious', not so certain. Keep in mind most goat vets know NOTHING NOTHING NOTHING about goats. It is truely up to the owner to learn ALL you can in the ways of vet care. You WILL be required to do most of your own. Get a couple good books and read up. Not knowing what shots and when or about 'contagious diseases' means you've got a lot of learning to do. But don't worry, that's half the fun AND we all started about where you did.
And even if your other goat that died didn't have a contagious disease, you can't know that this new one isn't bringing any in. Ask the previous owner about any abscesses they'e had in their herd, and DON'T BUY if they don't have untested animals that have had abscesses. CL is a horridly zoonotic (all mammals can get it, including you or your children) and horridly contagious disease that would just lead to more hearbreak. CAE is more manageable BUT is still a pain.
As for a 'bottle of what' that she will need, she is probably a bottle baby. She will still need 3 feedings 3x per day until about 12 weeks, then she can be tapered off. Lots of breeders wean at 8 weeks but I would NEVER wean a doe that young. They need at least 3 months of milk in most good breeder's opinions. Just feed her whole vitamin D cow's milk from the store, 12 oz per feeding (x3 = 36 oz per day) and use a lamb nipple on a pop bottle. NO replacer, it's bad for them. But, if she was dam raised she will NOT take the bottle, in which case it is ok for her to have a cup or so of grain PER DAY. I'd feed a good dry mix and mix in 1 part calf manna to every 3 parts or so to make sure she grows well. They don't need a lot, don't overfeed her. After she hits about 4-5 months, wean her off the grain. Goats don't need grain unless in late pregnancy (last month), or producing milk. Otherwise grain is unnecessary and bad for them. Free choice hay, of course.