I have a spirited child who can be very challenging in her own ways, though different from your exact experiences. I recommend starting now doing some reading about homeschooling, the time between now and school age will fly by and you need to feel good about your decision long before you have to make things "official".
Personally, with this type of child, I prefer unschooling. I follow dd's lead about what we learn about so as not to have those fights. Also, remember that your dd is probably learning a lot from you, even if she doesn't "perform" for you. You counting her toys and such will stick in her brain, even if she doesn't say it out loud. And most likely that is part of the reason she's now counting- not because of a handful of hours at preschool.
I would also look for classes/activities with other children that you will do when she is school age, as it sounds like she enjoys learning in a group. There are dance classes, music lessons, some times local children's museums, or nature centers will offer classes.
Hope this helps!
Laura, Mama to Mya 7/02, Ian 6/07 and Anna 8/09