Denise,
I would take the job. Sounds like you are
6D with 85 if there is enough room. Shutter at top sync speed in MAN. f-stop as high as possible. Flashes on MAN full power. Play with exposure till you get it right.
580EX in soft-box and 430 in umbrella. Each light basically on each side of you slightly above.
I had a cat once that would blink to the pre-flash so I could never get eyes open till I went MAN.
Find a simple but loud noise maker/clicker. Nothing to scar the pet but to perk the ears and eyes. I have a little from that if you squeeze it will make a loud click sound. Works great to make ears and eyes stand up.
LOTS of patience.
Have fun.