Vivi and Carrot will hit it off as fellow sovereigns, since Carrot is the New World Vivi parallel, I just never put it together because I didn't really view Carrot as Royalty. If you do, stuff makes more sense, and you can start to see a lot of parallels and connecting themes between the two characters.
-Vivi and Carrot attacked the crew upon meeting them while in/on a giant animal (Laboon, Zunesha). They then sail with the crew in a slightly suspicious way
-They have an overall goal (get to Alabasta/Wano) but have to go to a bunch of other smaller islands first (Little Garden, Drum, then Totto Land just... uh... being a shitton of islands close to each other)
-Despite being strong for their age, Vivi and Carrot were too ignorant about war and death. Vivi gets punched by Luffy for being too idealistic about keeping people from dying in a war; Carrot learns how dangerous piracy is when Pedro sacrifices himself to save her and the Straw Hats.
-Both of their countries were destroyed by a powerful pirate looking for information about the Void Century, with Alabasta being dried up by Crocodile, and Zou being ravaged by Jack the Drought
-Both are associated with jumping (Vivi's final attack against Mr. 6 and Ms... Father's Day??? I forget her name, and her leaping off the ship before the Reverie), and using close ranged attacks with odd hand-based weapons (Vivi's Peacock Slasher, Carrot's Paw Gauntlets)
-Both have had their mentor die in the Post Time Skip (Pedro and Cobra)
-Both are connected to Pluton, as Zunesha is meant to destroy Wano's borders to unleash Pluton, while Vivi's country, Alabasta, hid the information that Pluton existed in Wano