This is a myth. There are a HOST of reasons why a dog should be spayed before it gets its first heat, the biggest one, by far, to prevent unwanted pregnancies.
I spent three minutes, and found this information readily available:
*In the United States, most dogs are spayed between 5 and 8 months of age. Many animal shelters and veterinarians are starting to spay female animals at a younger age, even at 2 months. This early spaying does not affect the growth rate, and there are no appreciable differences in skeletal, physical, or behavioral development between those animals spayed early than those spayed at a more traditional age. It must be remembered that younger animals may need different anesthetics and are more prone to hypothermia (lower than normal body temperature) during surgery. As long as procedures are modified to account for these differences, early neutering is very safe. In fact, animals spayed at a younger age often have faster recoveries than those spayed when they are older.
Then this:
•If your dog has not yet had her first heat, consider having her spayed before that occurs and you can avoid the complications that arise if she is spayed while in heat or that can occur if you wait until after she has been in heat to have her spayed. A common misconception lingers that a dog should not be spayed before her first heat cycle. There are actual health benefits, such as the decreased likelihood of certain types of cancer, if a dog is spayed before her first heat. An infection of the uterus called pyometra can also occur in dogs and cats a few weeks after their heat cycle ends. If the pet is spayed before her first heat cycle, the possibility of this life-threatening condition can be eliminated. The spay surgery can generally be performed at any point after a dog is 8 weeks old, though about 4 months of age is often considered the ideal time.
Two separate sites, biased? I think not. But, in case you are not convinced, THIS material is straight from a BREEDERS site.
http://www.breeders.net/k9-articles/.../dogs-in-heat/
When should I spay my dog?
If you are not planning on breeding your dog, it is best to have her spayed prior to her first heat cycle. Doing so is protective against many types of cancer later in life. Many shelters insist on spaying all dogs before placement so spaying may be done as early as six to eight weeks of age. At traditional veterinary clinics, it is much more common to spay at six months.
One common myth is that a dog will somehow mature better if she is allowed to go through one heat cycle prior to being spayed. In fact, there is no such advantage, and waiting to spay your dog actually puts her at a disadvantage because she is at a much higher risk of developing mammary cancers later in life.
Another myth is that your dog should be allowed to have one litter before spaying so she will be a better pet or so your children can experience “the miracle of life.” Again, not true. There is no advantage to having your dog reproduce before spaying her, and your children might be much better served by spending time working at a shelter to experience the misery of abuse and neglect suffered by unwanted puppies.
Here is a sad fact from the Atlanta Humane Society, one which is mirrored at most other shelters in large cities: “20 tons of dead animal bodies produced in one year in the Atlanta Area alone.” The moral of the story? Don’t breed your dog unless you have good reason to, such as furthering the breed for show or competition purposes by conscientiously and responsibly pairing dogs who are prime examples of the breed standard.
Back to the OP- I know she is your daughter's dog, and she is still trying to make her way out in this big world, but, please continue to do what you can to see that Zoe gets into the clinic!!!