You can brew the batch and haul it. It would be a tight time frame, and the beer might not be able to age to give you a great taste. However, what I would recommend doing is, creating a yeast starter for a day or so, to get the number of yeast up really really high. Which should speed up your fermentation process to a few days.
I would then boil some water with your priming sugar, and put it in the bottling bucket before you siphon your beer to your bottling bucket.
Then when you bottle it, I would suggest wrapping each bottle in a little news paper, and then place it in a 24 pack box (one with the dividers in it like sam adams or something).
I would then put it in a place for the remaining days to carbonate, and the carbonation should be done after a week. When you do put them in your car, just to air on the side of caution, I would wrap each box that has the beer in one of those big black trash bags. One of the ones that are meant to have yard waste, so that it is harder to puncture the plastic should one of the bottles explode.