Pregnancy coverage might be a huge issue for you. It might be difficult to find an insurance company willing to cover you for maternity with an already diagnosed pregnancy. Without at least 80/20 maternity coverage guaranteed in writing, and signed on the dotted line, DO NOT GO until after you have the baby.
Your family coverage should be at least 80/20 and with low personal and family deductibles and low out of pocket limits per year. You should get the highest prescription coverage possible with no exceptions for medications such as asthma meds and no caps on hospitalisations.
What sort of visa are you entitled to get? Will you be able to work? Will DH's visa be linked to this particular job? Be aware that South Carolina is an 'at will' state, meaning that employees can be fired for any reason or none, and if DH gets fired you may have to up sticks and leave, so you need to have contingency plans.
You should really try to nail the HR dept down about a relocation package and support once you get there.
You should investigate schools before settling on a house or apartment. You will need to find the best possible school and then find a residence in-district.
Go online and see if you can find any kindred spirits before you go, if you go in the end.
Between yourself and DH, I would say you should go with an exit strategy and timetable in mind, rather than leaving it open ended. Have a date at which DH will be looking for another job or another move. That way, if you don't like it at all, it will be up to him to persuade you to stay and not the other way round. If you do like it and he is going to be kept on, then he can do his best to stay, extend the visas, etc.
SC is by all accounts very pretty, but the general culture would give me pause I must say.