If you guys really wanna know, I see Carrot more like a sister or a daughter. After all I spent more than 7 years analyzing this character's journey so she had an impact on me. But not in any weird way, I see Carrot as a second apparition of Luffy. She reminds me the old time. When I was first reading the story.
Furthermore, this character is a storytelling abnormality, it should not exist in the realm of One Piece. That's why I find Carrot so interesting.
This is exactly why I love Carrot's character.
She really is the Luffy of the New World on some levels.
Inspired by Pedro, Roger, the Straw Hats, and the legends she had heard, Carrot ventured out into a sea she knew nothing about, thinking a few carrots would be able to keep her full and refreshed the entire journey to Totto Land. Carrot fought her way through Whole Cake with kindess and curiosity, until Pedro died. Like with Luffy watching Ace die, she changed, but became more focused on revenge.
Carrot and Vivi are the only Straw Hats who will join the crew AFTER their inspirational figure died.
Carrot's earnest joy in exploring the world, only to be smacked in the face by how cruel it can be, really reminds me of Luffy in the pre-time-skip so much. I hope Carrot can overcome that pain, and become strong and happy like Luffy.