Don't you mean "becomes a paladin" since half-goblin isn't really something you become in this context?
In any case, you might want to consider what the goblin equivalent to a paladin is, or consider having your character try to join a paladin order, because paladin is a word with a rather specific meaning. Why not just call her a knight?
In this setting, there are a pantheon of deities that preside over the classes of the world. Those who become paladins adhere to the deity of the paladins. It's kind of similar to the system of Wakfu when it comes to classes.
So, the half goblin protagonist instead of choosing a typical goblin class takes up being a paladin by pledging loyalty to the paladin deity. It would actually be different because goblin society tends to be on the chaotic scale of morality.

Even though I am kind of fond of the series, I actually would love to have a series that kind is a contrast to it's depictions of goblins. In contrast with how goblins are depicted as Always Chaotic Evil fodder in that series, this one still shows them as an underestimated race but one that is capable being good or evil like any other being. There are also female goblins, so they don't capture females from other species to reproduce.
The main character would be a half goblin, who lives with her goblin father and their clan in the caves. Due to her human heritage, she is bigger than the average goblin. Her mother was a human paladin that feel in love with her father and went native with the goblins. When she was three years old, her mother was forced back into the human world by her old order and she left behind her sword.
The main character becomes a half goblin herself, but dedicates her life to protecting her father's kind. She is also dedicated to finding her mother.