Buses generally start running to Magic Kingdom around 6:30am (others have said they can start to MK as early as 6-6:15am). Double check with your resort's front desk. You can catch the monorail from Magic Kingdom over to Poly. The monorail will take anywhere from 10-15 minutes, less if you catch one quickly. It stops at the Contemporary Resort and the TTC before going to the Polynesian. (FYI -buses to the other park begin running around 7:00am)
If you catch that 6:30 bus (be at the bus stop 5-10 minutes early just incase they come early) you should have plenty of time. We were about 10 minutes late to our Ohana breakfast in early December and had no problems being seated right away. (That was the same for the few other ADR's we were late to as well)
Enjoy your breakfast. We really enjoyed ours.