Hi MJ,
Thank you for caring for this cat.  It would be best to separate the cat and
dog until you learn more about how to keep the cat safe.  Let us know more
about your dog and what behaviors you mean when you say he "goes crazy." You
should be able to get a lot of good information here on how to introduce
them.
Depending on how well you have trained your dog, you might be able to keep
the cat after all.
Contact some rescue groups in your area and ask for help in introducing your
dog to the cat or, if you believe that your dog will not be safe for the
cat, ask if they can help with the adoption and explain the situation.
Most rescue groups are strapped for funds, so if you can offer to help with
some expenses, they are better able to help you find someone to adopt the
cat.
The cat may be microchipped, which would identify the owner.  Call around
and find a vet or rescue organization with a microchip reader.
Also, put a found ad in the newspaper (most of them run them for free).
Call veterinarians and ask them if any of their clients have called in to
find out if someone has brought in a lost cat that might have been injured.
Most veterinarians will allow you to put up "found and available for
adoption" signs.
If someone wants to adopt the cat, screen them carefully.  You can get some
advice about this from the rescue groups.
Good luck,
Annie

A cat that pretty and friendly must have an owner somewhere. Maybe
someone who's away for the holiday and will be missing the cat when they
get back?  Maybe contact nearby vets, humane societies, police, newpaper
lost & found in a few days to see if they get any lost pet reports.

If you can't find quarters for her soon (with a friend, or whatever),
take her down to ther Humane Society in Indianapolis.  If she is
friendly she has a really good chance of being adopted this time of
year.  It's way too cold there for her to be outside this time of year
for any extended length of time.

Good luck to you!
-L.