I have an exceptionally handsome & adorable 11-month-old puppy & would
like to find out about getting her into a TV commercial, movie, or...?
 How does one go about getting their pet a cameo on film/tv?

marty,

The Mecca of pet actors sites is Hollywood Paws:

http://www.hollywoodpaws.com/ask_anne/index.cfm?fuseaction=question&qID=95

In the Hollywood Paws "Ask Anne" column, Anne explains why pets don't
have agents, which would have been my first guess. It turns out that
movie and commercial directors only want to deal with a recognized
animal trainer, so these trainers are the gatekeepers for getting pets
film work.

A quote from Anne's column:

"The best thing to do is to find a film trainer who will help you
promote your pet and they can teach you and coach you with your pet on
set so that you will look like a pro."

That said, there are people who make a living (or try to) by telling
you how you can turn your pet into a star. One such example is:

Kay Cox - The Pet Counselor Talent Agency 

http://www.getnet.com/~petcouns/pettal~1.html

Kay writes "Pets that live in a high Movie, TV and Commercial Traffic
area and are pets that are highly trained are more likely to be called
for a job because they are living where the action is and because of
their unique ability to work with a crew and actors to get the shot
needed in the shortest amount of time."

For $50 she'll send you a "Talent Kit" for your pet.

There are even special workshops for training prospective star pets.

http://www.starpet.com/press.html

Interestingly enough, the article I'm pointing you to on the Star Pet
site includes the following snippet "Alyssa Polacsek, an editorial
assistant at Back Stage and an aspiring actress, saw a Back Stage
casting notice for a "small not-so-cute dog," to appear in a New York
University student film." So, it appears that the same magazines that
list work for human actors may carry advertisements for pet or animal
actors.

I'll conclude with a link to the National Alternative Pet Association
page that lists many animal trainers:

http://www.altpet.net/actor.shtml 

I wish you and the pooch a successful career.

Google Search terms:

"animal actor" agent

Thanks!!  Lots of intriguing leads & good info!!