I just saw your edit, skyward, so I'll add to my response accordingly, if you don't mind.
Home schooling can be harder for introverts, but if you can 1) join a homeschooling group, and 2) find a good babysitter (or two!)--especially one who can drive and who is willing to take your child to activities--it makes all the difference. This is experience talking! I'm an introverted HSer who couldn't survive without her HS group or her sitters!
Generally speaking, the ideal homeschooling group is a secular or diverse group, unless you are actually of the religion that the HSing group is. Trying to "pass" as a religion when you're not is usually not worth it, from what my HSing friends tell me. (I never had to go that route, since we have an active secular HSing group in town.)
As for the sitters, look for homeschooling teens or for college students who are available during the day.
As your child gets older, it does get easier to arrange drop-off playdates that don't require you to be social, but get your child plenty of time with friends. Be on the lookout for those!
Also, look into open gym time for preschoolers or classes that might interest her at your park department or local gym. Bring a book or some earphones and people will mostly leave you alone even as your daughter is getting time with people.
Even time in childcare at the YMCA or similar organization is good. 2 hours of childcare per day is free with membership at our local YMCA, so I get some time to myself and some exercise, and my kids can get some time with other kids. Everyone wins!
I hope that helps. It is possible to be an introvert who homeschools and get enough social time for your child without losing your mind. It just takes a little more planning and effort up front to get it arranged.
