Took me just over 6 hours last time, but Jacksonville had MAJOR road works. That probably added 15-20 minutes to the journey but it wasn't rush hour. Avoid I4 around Orlando at rush hour and Jacksonville gets pretty snarled up at times.
HH is a great place and has a lot of things to do BUT if you're only looking for a short "beach break" added onto a Disney/Orlando vacation I'd opt for Vero. Much nearer and a much longer season. HH bookings get pretty busy at high season, because it has a relatively short "peak time".