Scientifically speaking, evolution is not required for variations within a species. The only requirement is that all of the genetic information seen in the species today was present in the first generation. From then on, species experience the isolation of genes through geographic and other factors.
The breeding of new species of dogs does not produce new genetic information--it merely isolates particular genetic information that is already present in the species. This is a key point--selective breeding does not result in any new information, but actually the loss of information, as only the chosen genes are kept.
In cattle, selective breeding often results in weaknesses within a certain breed. Hereford cattle are quite susceptible to Pink Eye, but if you have Hereford Angus cross, the weakness in the Hereford Breed, that resulted in a loss of genetic resistance to Pink Eye, is merged back with the lost genetic information that is still present in the Angus breed, yielding a herd with higher genetic resilience.
Different breeds of dogs can still interbreed with each other, as can different breeds of cattle, so there is no new species and no evolution. Evolution is the creation of new species--variation within a kind is not evolution.
Dogs have, indeed, shown a higher variability than other species, but they are all still dogs. Another key point, though, is that this doesn't happen in nature, but with a great deal of intervention and unnatural forces brought to bear upon the process (by humans).
The word used in Genesis is probably best translated "kind". Noah didn't bring Chihuahuas, Poodles, Great Danes, Labrador Retrievers, Beagles, and every other kind of dog. He brought two mutts, which is basically what you get if you take all the breeds and interbreed them together to undo the genetic isolation.
Furthermore, Noah didn't bring a Chinese, a Korean, a Vietnamese, a Russian, an Arab, a European, a Jew, an African, and a Hawaiian. There were only eight people, but those eight people contained all the genetic information necessary to produce the variations we see today that have been caused by genetic isolation through geographic and other factors.
There are a lot of resources online about this. Here's just one.