Ah, this is one of my very favorite things to ponder in the entire literary world! : ) Fitzgerald is incredibly similar to Gatsby. In fact, I would go so far as to say Gatsby is Fitzgerald in symbolic form. Although there are a few differences, such as Fitzgerald's affinity for alcohol and writing, Gatsby and Fitzerald are more alike than different. Both Gatsby and Fitzgerald had some aspect of their lives that bonded them to people without breeding (Gatsby grew up poor; Fitzgerald was part "black irish"). Both Gatsby and Fitzgerald fell in love with a very rich young lady (Gatsby's was Daisy Buchanan; Fitzgerald's was Zelda Sayer). Both Gatsby and Fitzgerald became obsessed with that same young lady and remained obsessed for the rest of their lives. Both Gatsby and Fitzgerald tried to gain fame and fortune to win the heart of thier lady (Gatsby through bootlegging; Fitzgerald through writing). Both Gatsby and Fitzgerald were known for thier lavish parties. Both Gatsby and Fitzgerald would have been considered "West Eggers" in that they were not "old money." Both Gatsby and Fitzgerald lived on Long Island during the most significant times in thier lives. Both Gatsby and Fitzgerald died forgotten (Gatsby's funeral was unattended; Fitzgerald's literary career hadn't taken off).
In regards to "symbolism in the novel," I'm not sure you could point to an example proving that this similarity is what Fitzgerald meant to achieve. He has never admitted this. However, no one can deny the copious examples listed above. In addition, Fitzgerald's other novels and short stories contain examples of a similar nature. ("Winter Dreams" comes to mind.) If I had to pin down some symbols, I would say (very simply) that Daisy symbolizes Zelda and Gatsby symbolizes Fitzgerald. The most obvious example that this similarity is a reality, however, comes from the dedication of The Great Gastby itself: "Once Again To Zelda."