What is significant about Myrtle's questioning whether the dog is a boy or a girl?
I agree that Myrtle is not too bright if she has to ask the sex of the puppy. But looking at the context of the question reveals a little more of Fitzgerald's intent. First, the dog is called an "airdale", a word that closely resembles "airhead"--and a term that could describe Myrtle. Just before this, Myrtle has said she prefers a "police dog". Perhaps this is to protect herself from Tom. When the man doesn't have a "police dog", he offers Myrtle a dog which supposedly has a beautiful coat. Myrtle thinks the dog is cute--probably because the fur coat reminds her of the things Tom can buy her. But once Tom has purchased the dog, he says, "That dog's a bitch..." inferring Tom's attitude towards all females. Later that day, he breaks Myrtle's nose.
In this part of Chapter 2 of "The Great Gatsby," the author is using a simple exchange between Myrtle and Tom to demonstrate the intelligence level of Myrtle. When Tom buys the dog for Myrtle and she asks if it is a boy or a girl she is showing everyone that she is not too bright. She is simply a "toy" for Tom. He is not involved with her because of her mind. He is strictly using her for his own needs and desires. It should be a very simple matter to determine the sex of a puppy, but Myrtle doesn't have the presence of mind to simply look at the belly of the puppy and determine that for her self. This goes to the characterization of a woman who is not too bright.