Should you be interested, the Adventure Cycling Association has created bike routes all over the US. One of them, the Atlantic Coast route runs from Philadelphia down to Savannah, GA.

Given the route you outlined, you will have more than enough, indeed too much, time to complete it. Are you intending to spend time in various places along the way or do you intend to ride the entire 3 months?

I recently rode from Charleston, SC to Lambertville, PA in under a month averaging about 50 miles on 20 biking days. I spent the rest of the time visiting places.

Since you haven't done a long bike tour before, I'd recommend that you gather your gear together and try some over night rides to a nearby town/campground to see how long you can ride in a day. What you learn on these trips will be the basis for the trip you've outlined above.

Good luck!

Ray