Definitely drive. Not only is it allowed as long as you don't try to go inside MK from there, but you'd have a long journey from AKL to WL using Disney transportation, since there are no direct resort-to-resort buses. I would still recommend making an ADR for Whispering Canyon. You don't need to do it 180 days out, but calling earlier that morning or even the night before is well advised. It can get crowded, even at breakfast.
Also, make sure you still have your parking pass from AKL on your dash. You'll need to drive through the MK gate to get to WL. When the gate attendants see the pass, they'll generally wave you through without even asking. You'll need to stay to the right at the gate, and then veer to the right turn off lane as soon as you're beyond the gate. Stay straight on that and it takes you straight to WL.