towing with water is a debate similar to towing with the gas on.
I personally avoid doing it because it adds weight
.. reducing milage and increasing wear and tear on my tug.
The slosh factor also is quite noticeable with my set up (Small tug, big trailer)
My last trip out I had forgotten my shower pump for transferring water from campground filled rolling water tote to my tank. I simply poured water into the tank by hand with a funnel. Took a little longer, but there are many ways to bathe a cat...