"NORMALLY" the Resort Monorail begins about 6:30-7:00AM.
BUT lately, it has been subject to later opening times (8:30AM) on selected days.
I'd recommend that if you have a very early breakfast at a monorail resort that you park at the resort during breakfast.
You COULD pay to Valet Park at the resort and leave your car there all day, if you are headed to MK that day.