Some thoughts based on the perspective of someone who's never really owned a car. I can't imagine going to all the hassle of finding a car, buying it, transferring ownership, insuring it, just for 5 months. Regarding the points you raised:
1. Seeing your husband: Greyhound seems to have 3 buses a day going from Columbia to Charleston. Regular price $28.50 one way, advance purchase price $14.50. Not sure where you are with respect to getting to the bus station, but taxis are always an option if Columbia public transit is less than ideal. The intercity bus takes 2.5 hours, only 30 minutes more than driving. And you can get a lot done on a bus (reading, working, e-mailing, etc) since you're not distracted by driving. It may add up,but it's got to be less than $10,000 plus gas and ownership costs.
2. Dog emergency: As you say, your friends can help out in a real emergency, which would be infrequent enough that you wouldn't be imposing. For something with a bit of lead-time, pet taxis can get you to and from the vet, for a lot less than the price of a used car. There's at least one company in Columbia (
http://awayhomeandpetcare.com/services/pet-care/pet-taxi/). I imagine there are more if you spend the time to look. You could contact them to see how quickly they can respond in an emergency. Also talk to your vet - you never know, they might have some sort of pet ambulance thing going on.
3. Regular life: You seem to be set up for getting around without a car for work, groceries, etc. I see Columbia has a "humid, sub-tropical climate" -- being from Canada, I don't know anything about that, but it doesn't strike me that weather should be a problem unless there's a hurricane, in which case you shouldn't be out at all.
4. Unexpected, one-off events: Bike, public transit, friends picking you up, and taxis should all be enough to deal with these for 5 months.
5. Safety: I can't advise - I'm a woman who's lived on my own in a house with no car in the driveway for years and years and it never even occurred to me that the lack of car was an issue, but I have no idea what the situation is like where you are so you'll have to be the judge. If the car is really the only thing making your house looked lived in, maybe you could ask a neighbour with 2 cars if they'd be open to parking one of them in your driveway for the 5 month period? Or is it worth to advertise your driveway as parking space on Craigslist? You never know, maybe there's someone close by with 5 cars desperate to find a place to park one of them....
It seems to me that 2 of the 3 issues (husband and dog) are resolvable quite easily, but the 3rd (safety) is up to you. Good luck!