What is the significance of the puppy? Why do you suppose Fitzgerald included it as an element in chapter 2?

The man from whom Tom Buchanan buys the dog "bore an absurd resemblance to John D. Rockefeller," a point that seems all the more notable in a book that emphasizes the difficulty, even the impossibility for some, of attaining the American Dream: the idea that any American, through hard work and perseverance, can prosper.  Certainly, to compare, in any way, a man selling dogs out of a basket on the street with Rockefeller is unexpected, but, here, it seems to be a statement on impossibility of the dream for this man: he may work hard and even look just like a millionaire, but he will never be able to reach that level of prosperity and influence himself.

Further, Myrtle Wilson's total lack of concern for her new puppy, once she'd sent someone for a box of straw and saucer of milk, is appalling and cruel.  It sheds a great deal of light on her character.  She wants things, she wants to have things, and she wants Tom to buy them for her.  She's not, however, interested in responsibility, and she is certainly not a kind or compassionate person.  During her party,

"The little dog was sitting on the table looking with blind eyes through the smoke, and from time to time groaning faintly."  

This dog is so young that she can hardly see, if at all.  She is surrounded by loud noises and loud people that she cannot see, without anyone to hold her or pet her or reassure her, and Myrtle is completely oblivious.