You will be just fine. No GED will be required.
I helped several students over the last few years apply to college as homeschoolers - no school ever asked for any documentation from the state or anything and none required any diploma or anything. They did require a transcript and complete course descriptions about what courses they took. Just realize though that the SAT and subject tests or the ACT with writing weigh a bit more in your case.
And like the post #6 above - they too got into the Ivys and everywhere else.