Is there a way for players to create a character whose race originally has hit die of it's own, such as dragons?
According to Monsters as PCs:
For monsters with racial Hit Dice, the best way to allow monster PCs is to pick a CR and allow all of the players to make characters using monsters of that CR. Treat the monster's CR as its total class levels and allow the characters to multiclass into the core classes. Do not advance such monsters by adding Hit Dice. Monster PCs should only advance through classes.
If you are including a single monster character in a group of standard characters, make sure the group is of a level that is at least as high as the monster's CR. Treat the monster's CR as class levels when determining the monster PC's overall levels. For example, in a group of 6th-level characters, a minotaur (CR 4) would possess 2 levels of a core class, such as barbarian.
However, the rules warn that most monsters are not ideally balanced for use as player characters, and GMs need to use a substantial amount of judgement. It's not a fixed thing like D&D 3.5's ECL system, which provided unambigious rules for playing many monsters, but had similar balance and gameplay issues.