How long after RAI treatment can I travel in a car with a passenger?

Hi Folks

I just joined and wonder if someone might answer this question. I am having the radiation drink in the London Ontario radiation department. I will be on their diet and receive two injections prior to the "drink"

I know that I will be a hermit with precautions for a few days after it but we want to travel to Florida as soon as I am safe. I will also have a 6 year old puppy in the car. Has anyone done this before and can explain the guidelines they were given? It's been quite a year but I'm gonna lick it.