No, Luffy cares about Carrot. He actually likes her. He gives "zero fucks" about Yamao, the character's name he can't even be bothered to remember and set on babysitting duty last chapter. But he actually likes Carrot. Has offered to share delicious food with her (a notable thing considering Luffy's personality), he saved her from Katakuri, and he entrusted her by name to look after his ship for him whilst he was gone. Sure there is room to grow with their relationship, but that can happen whenever. And Carrot's already well accustomed with many others in the crew.
Luffy's yet to see Carrot do anything amazing, unlike the others who were all lost for words at seeing her Sulong form. Now every mink is going Sulong EXCEPT Carrot (who is right next to him atm), meaning hers is being saved for a special moment. Luffy can grow from liking her, to really loving her at the drop of a hat after seeing that.
Give me one memorable Moment with Luffy and Carrot in it
Luffy/Zoro: Frees him
Luffy/Nami: Help me in Arlong Park, gives the strawhat
Luffy/Usopp: Entire fight against the cat guy and post, Enies lobby and W7
Luffy/Sanji: Baratie/WCI
Luffy/Chopper: Drum Island flag
Luffy/Robin: I want to Live
Luffy/Franky: Chase with underpants and sunny build
Luffy/Brook: Let me get your shadow for you, don’t be strangers
Luffy/Jinbei: “Luffy-kun” “Ace” “Fucking Marineford War
Luffy/Yamato: debatable, don’t think she’s joining but she’s had more moments in two chapters with Luffy than entire history of carrot being present
Luffy/Momonosuke: Since Punk Hazard, trash can, Zhou, Wano speech, onigashima capture
Luffy/Kinemon: More personal moments
Luffy/Whitebeard: I’m gonna be pirate king, information exchange, stand on equal terms
Luffy/Rayleigh: 2 years
Luffy/Law: race to the Donquixote tower and doffy fight
Luffy/Aisa: the little girl in Skypeia had more conversation with Luffy within the snake