I have make frame and panel doors using the router table and door making bits. Even with plywood panels on the inside, when doors get to be large they become less stable.
To increase your odd of having flat stable doors, plane to final thickness and let this wood acclimate preferably in you house, for a few weeks. Then rip to final width and acclimate again. Any warping or bowing will be noticable after the acclimation period and you can cut around or discard these pieces.
It seems like a lot of trouble but it is easier than remaking the doors multiple times. I will say Oak is pretty stable but you should at least let the wood sit for a while after cutting because that is usually when any type of warpage will happen.
Where are you getting you Oak?
Steve