Is this 48w travel fridge a 120v dorm type fridge?
I have one in my TT and it draws about 80w at a 1:5 duty cycle at about 80f ambient. Also, the locked rotor draw at startup is significant. It was necessary for me to go to a 1000w inverter to handle the startup draw. I haven't done any exact daily amp hour measurements but I have my solar system at 235w module with 320 AH of capacity.
A possible better solution, if you wish to travel without a generator would be to find a cheap camp site that offers electrical and pull your power off the pedestal.
IMO, a single battery and 100w of solar is not going to cut it.
If you discharge one of those marine/starter batteries continually until it is discharged (probable in your use), it won;t last a month. If you want to have electric devices running every day, you'll need to have more battery capacity and if you want to charge those batteries with no generator, you'll need more solar output.