Jeff--
Sorry for the delayed answer -- I just got back from a 2 week backpacking trip with the Boy Scouts in northern New Mexico, followed by an immediate turn-around back to Colorado for the SSE conference. But I'm home for a few days, so I'll take a (very belated) stab at answering your question.
First, sorry to hear about your cat -- in the several days since you posted, hopefully the incident has come to a happy conclusion. I also commend you for trying to figure out how to do this yourself -- usually when people contact me for missing pets, they want me to find the cat or dog (or goldfish?

for them. In most cases I have to turn them down.
First, the most expeditious way to apply dowsing in this case is to get a map of the area no larger than the limits of where the cat could possibly be (this will take some judgment on your part, as the cat could theoretically cover quite a lot of terrain -- but in practical terms probably wouldn't). Then just dowse the area. Of course, this doesn't necessarily help the AOL problem. If you find that is problematic, go ahead with the blank sheet approach, and you could use either a matrix or triangulation. However, an alternative might be the "Zeno's paradox" approach, where you dowse which half of the map the cat is in, then which half of that space, then which half of the still smaller space, and so on.
Finally, rather than a a tasking of 'where will the cat be' you might want to phrase it 'where should I go to recover (or find) the cat?' Also, of course, the more specific on the cat's identification you can be, the better, such as 'where should I go to find our beloved Snookums,' or whatever.
Good luck!
Paul