Welcome to the forum Alex, you will get all kinds of help and information here. Only you will know if an RV will be to small for you, your girlfriend, two dogs and a cat.
I suggest something used with a walk around bed, a kitchen and or living room slide. Also a 5th wheel costs more than a travel trailer but a 5th wheel has more storage and separates the living area from the bedroom.
This would be one way to get into RVing and help you with your taxes too. You can deduct the interest you pay just like on a sticks and bricks.
I would do it, I did it for six years and we had winters not like Alabama. Good luck with what ever you decide.