The carrot itself is fine; its hardness is the issue
Carrot is not a toxic food for kittens, and a small amount can be offered safely, but the form decides whether it is a treat or a hazard. A kitten's teeth and jaw are built for small, soft prey-sized bites, not for crunching through a raw carrot baton. Hard pieces can break into awkward chunks that are difficult to swallow and easy to choke on.
Cooked carrot solves the problem neatly. Steamed or boiled until it gives easily between your fingers, then chopped fine or mashed, carrot becomes a soft garnish a kitten can eat without a struggle.
What a kitten can and cannot get from carrot
Carrots are known for the orange pigment in their flesh, but a kitten's body is not set up to convert plant pigments into usable nutrition as efficiently as some other animals do. Her essential nutrients come ready-made from animal-based kitten food, which is why carrot should be understood as texture and interest rather than a vitamin strategy.
The fibre in a little cooked carrot can be a mild digestive plus in tiny quantities, and some kittens enjoy the faint sweetness of the cooked flesh even though cats cannot taste sweetness the way people do; smell and texture are doing the persuading. None of that justifies large servings, and a kitten who ignores carrot entirely is missing nothing her complete food does not already cover.
Preparing carrot so a kitten can manage it
Peel and wash the carrot, cut it into small coins, and cook them plain in water or steam with no butter, oil, salt, or glaze. Test a piece between finger and thumb: if it squashes without effort, it is ready for kitten-sized chopping. Cool it completely, because a small mouth is easily startled by hidden heat.
If you prefer raw, grate it finely and offer a pinch, which gives her the flavour in strands too small to obstruct anything. Never hand a kitten a whole baby carrot to gnaw as entertainment, and supervise any new food the first few times so you can see how she handles it rather than finding the evidence later. Cooked carrot also freezes well in an ice-cube tray in tiny portions, thawed one at a time, which suits a food she should only meet in garnish amounts anyway.
Watching the result of a crunchy experiment
After a first serving, check that she chews comfortably and that her stool stays normal over the following day. Gagging on a piece, pawing at her mouth, or drooling after eating any firm food means stop and look in her mouth if she allows it, and contact your veterinarian straight away if she is distressed, coughing, or struggling to swallow.
For ordinary digestive grumbles, loose stool or a skipped next meal after over-generous carrot is a sign the portion was too ambitious. Return to plain kitten food, and mention ongoing appetite loss to your veterinarian promptly, especially in a young kitten. Kept small and soft, carrot rarely causes drama.
Logging which garnish foods she handles well is easy in KinsLe, because Care Teams keeps those small discoveries with her daily feeding assignments for everyone in the household to follow.