This is what I found:
There are few other exceptions in addition to what you mentioned: Dogs and cats may be exempt if a veterinarian certifies the animal is in poor health, ill, too young, or too old, or should have the surgery only after a specified date.
I would consult your Vet and get a letter regarding the need for her growth plates to finish forming.
Also, after passing a mandatory spay/neuter ordinance earlier this year, Los Angeles failed to provide its Department of Animal Services with any funds to enforce it. The city controller has announced the Department will rely on voluntary compliance.
http://www.animallawcoalition.com/spay-neuter/article/369
I also found this:
http://animalcare.lacounty.gov/cms1_045463.asp#TopOfPage
Competition dogs. A Competition Dog is a dog which is used to show, to compete or to breed, which is of a breed recognized by and registered with the American Kennel Club (AKC), United Kennel Club (UKC), American Dog Breeders Association (ADBA) or other approved breed registries. The dog or owner must also meet ONE of the following requirements:
The dog has competed in at least one dog show or sporting competition sanctioned by a national registry or approved by the department within the last 365 days; or
The dog has earned a conformation, obedience, agility, carting, herding, protection, rally, sporting, working or other title from a purebred dog registry referenced above or other registry or dog sport association approved by the department; or
The owner or custodian of the dog is a member of a department approved purebred dog breed clubs, which maintains and enforces a code of ethics for dog breeding that includes restrictions from breeding dogs with genetic defects.
(So, if you're not already a member, I'd join the NCA! You only have to meet one of the requirements and that would meet it. )
