DS4 was accepted to enter Kindergarten early in private school. (Misses it by 8 weeks)
However, there was extensive testing and the only reason I think they allowed to even entertain the thought was because we managed to get him early entrance into PreK-4 last fall. My argument was he had already done PreK-4 so please test him into Kindergarten so he doesn't have to do PreK-4 all over again. He passed the test with flying colors.

For your situation, since you have already "home schooled", is to continue homeschooling and focus on your DD's "weaker" points so she can master them by the time the next school year rolls around. THEN try to get early entrance into 1st grade next year.

Being EG and the oldest in the class just seems to be a recipe for disaster. We are concerned enough about the fact that DS will not even be close to being challenged, even though he IS accelerated.