Interesting! I went to look up meacan and find it means a "tuberous root", so it can be used with something else to mean all sorts of things: meacan bán - parsnip; meacan biatais: beet; also meacan an phobóil - butterbur (what in heaven's name is a butterbur? Well, it's one of these: http://tinyurl.com/npgelg6
I think at this point the sentences may sound a bit stilted in English because this is very beginner-level and these sentences will help us understand the differences between the English "a" and "the" in Irish, as well as singular vs plural. So, we have to watch out for whether or not there's a "an" or a "na" in front of the noun. You will be marked wrong if you forget to include the definite article in exercises that want you to translate "the carrot" vs "carrot", as I know from experience because I'm often so hung up on getting the noun spelled right that I forget to notice whether there's a "the" or not in front of it.
Feels like people are giving this response a hard time but I do agree with it, at least a little. Might have been more useful to teach us: "I have the carrots" or "We have carrots".
Working in a restaurant, I've absolutely said those two. Either way, it's a useful example for how the grammar in Irish works, I just wish the example given here was a little more practical.
Duolingo isn't a phrasebook - the purpose of the exercise isn't to help you hold down a job in a restaurant, it's to help you practice the grammar. If you know how to say "I have the carrot", then you know how to say "I have the money" or "I have the key" or "I have the answer".