How Long Will This Battery Keep My Fridge Powered For?
There isn't enough information to answer this, because your fridge's specs only tell the maximum power draw. 

I presume it draws this power when the cooler is running. But it is not running all day. So you should check for how many hours the cooler will run in a day, how much energy it will use... This depends on outside temperature, the quality of the insulation, etc... many variables, and many unknowns.

Say you have a box and you want the contents to stay below 5°C. So you install a cooling system. You also install thermal insulation. 

What is the compromise? You could install a foot thick insulation, and then you'd need a tiny cooler to compensate for the losses. Or you could use just a little bit of insulation, like an inch of foam, and use a more powerful cooler.

I'm trying to tell you that your question is a little bit more complicated than you think.

Fridge manufacturers usually do not quote an average power, because it depends on ambient temperature, and also it depends on user habits, like how often you open the door and let warm air in, if you place a warm beer inside and expect the fridge to cool it, etc.


  assuming I sleep in the car for approx. 8 hours a night and drive for the rest of the day


In this case, the most cost effective thing to do is not to store electricity, but to store cold. If you have a power supply available all day except during the night, then the best option is to put a few gallons of bottled water (as thermal mass) in your fridge next to your sensitive medicine. 
When you have power, the fridge cools the thermal mass. When you don't have power, the thermal mass absorbs the heat flowing though the insulation.

The good thing about a few gallons of cold water used as thermal mass is that it doesn't break down, doesn't need maintenance, it can't fail. Even if your car dies, your fridge dies, and everything stops working, you still have time to find someone who owns a freezer, or buy some ice, whatever. It is low-tech and foolproof.