I would put louvres high in the door and a take-out fan in the window. This draws air from the house through the darkroom and out of the window. The cats would be safe, since the chemically laden air would go straight out, not back into the house.
Also I would put a slightly more powerful fan in the door, so as to blow in more air than the window-fan would take out. This creates an overpressure inside the darkroom that might help keeping dust out (not sure if that would make that much difference, but I'm planning it for my darkroom anyway... if I ever get around to building it)
Also, make sure you don't suck up cats hair that end up all over your negatives... ;-)
Useful information might be found here (scroll down to see more articles)
EDIT: the above link is problably not as useful as I though. The next link might provide more detailed information:
Also, I would look into using DIY materials like fans and ducting designed for removing moist air from bathrooms and such, they should also be suitable for darkrooms and might be less expensive overall.