I'm all for public school if you can make it work. Dn't give up if you can see a way to make it happen that will be good for your child!
But if not, it is possible to homeschool an HG+ child. In elementary school, it's really not that hard. You know more than you think you do!

Plus you don't have to know *everything*--public school teachers don't! You just have to know how to find answers. Bonus points for teaching the child how to find answers himself!

As your child gets older and starts to outstrip you in various subjects, your job shifts from teacher to guidance counselor, helping the child to find learning opportunities, classes, mentors, resources, etc. Plenty of parents homeschool PG kids even into high school. It can be done!
Single parenting and homeschooling is more difficult. Ideally you would want to find child care that could also handle some of the teaching load. Maybe you assign "homework" and the child completes it during child care hours. But it can be done.
Don't get overwhelmed, regardless of what you decide to do. There is always a way to make things work. It may not be ideal, but there's always a way.
