My fiance and I are moving to Sydney Australia from San Francisco at
the end of September and would like to bring our dog(~60lbs) with us. 
We have done some initial research on transport companies that will
facilitate the dog's travel by air, but we would like to explore the
idea of taking the dog by boat.  Ideally, I would like to ride with
her on the boat.  Are there any companies that offer this service, how
much will it cost, and how long will the trip take?

With the exception of service animals, no major cruise ships allow
dogs in the cabin with people. However, Cunard's transatlantic QE2
allows small dogs in the ship's kennels (dogs are not allowed in the
cabin). The dog must be fairly small as the kennels are only
33"x33"x29". The kennel has visiting hours three times per day.
http://www.h4ha.org/library/traveltips.html

Puppy Travel, the pet travel agency provides information and services.
http://www.puppytravel.com/transport_relocation.html

Most of the countries the cruise ships visit have strict quarantine or
entry requirements for pets. Secondly, cruise ships generally have
very strict health codes to follow as well as poor accommodation
configurations for pets?separate areas where pets can exercise,
relieve themselves, etc?

Nenna-GA

This may be of interest to you:

http://www.pet.net.au/pet_travel.htm

"Entering Australia... you will need to have your pets in Quarantine
on arrival. This can last from one to several  months depending on
your pre-travel preparations and country of origin. One month is now
quite common reducing stress for the animal and costs for you. Get all
your pet's vaccinations and papers set up so that you can retrieve
your pet at the earliest possible time. Quarantine is usually in
Sydney or Melbourne. See www.aqis.gov.au for information on
requirements. Your local quarantine/customs people will need to seal
your pet crate - if there is delay involved in travel the seals may
need to be removed for the animal's comfort needs. Re-sealing will be
at your own  expense. Check timing carefully when planning your
travel."