Self-scoring IQ tests are only indicative of high ability and are not considered to be scientifically valid. I always think it's valuable for parents to have some valid measurement of their child's ability to help plan for their academics accordingly. Prior to homeschooling, did he have any group achievement tests administered in school? If so, you are entitled as a parent to see those results.
If you do choose to have him privately tested, this can be a costly event. You could contact a local university with a psychology department and see if they are willing to test for a reduced fee in exchange for allowing well-supervised graduate students to conduct the testing. If any learning problems appear, that is another situation in which parents should have diagnostic testing done so that they can best help their child. Since your son does not appear to be in any immediate need, you can consider testing for the future and "shop around" for the best affordable situation. Good luck.