Via taxicab. As long as they don't keep the cab waiting for them, round-trip shouldn't much more than $10 - $15. I know that seems like a lot, but lugging diapers and babyfood aboard a plane is worse, IMHO.
You could also check out the bus schedules for the area. Maybe LYNX runs between the airport and Lake Fredrica center....I just don't know. We always rent a car while in Orlando.