There was a mistake with some brackets in the Incubator that I just fixed. Really, the only correct translation for this is "I eat a carrot" (if you wanted to be more literal, you could omit the indefinite article, but then it's not correct English). "I eat carrots" would be "Ithim caréid"
http://www.panningtheglobe.com/wp-content/uploads/2012/11/moroccan-carrots-web.jpg Couldn't I say "I eat carrot" eating a salad like this? Some unspecified amount of carrot
I could also imagine making a carrot cake and, worrying about allergies, asking someone 'do you eat carrot?'. So what's normally a count noun can be coerced into a mass noun interpretation, but that doesn't mean it's the normal usage. But I have no idea how you would express this meaning in Irish.