I home school one dd. A lot of people in our home school groups have only one child, so Zayis is not alone there.
I don't really do any extra planning or thinking because of her only status. But I also live in southern CA where there is tons of stuff for homeschoolers to do, so maybe that's why I've never had to worry about it.
She does park day Mon, the beach on Tuesday, ice skating classes on Tuesday and Sunday, voice lessons on Wednesday, and usually at least one other play date and a field trip (with other home schoolers) during every week as well.
We could do more lessons or more park days, but she's just not all that social and likes being at home (especially in the yard by herself playing with bugs and the animals).
The only time I feel stressed or over scheduled is when I'm doing too much myself on top of her schedule. I'm a single mom and I'm a full time student, plus I work part time. So yeah...that's a lot lol. But I do it because homeschool is actually easier for me than trying to keep to the public school schedule. And she loves home school too. She's never complained about being lonely, and rarely says that she's bored.