"She is a military doctor."
Translation:Is dochtúir míleata í.
Because you don't use the verb bí when using one noun to describe or categorize another noun (or pronoun), you have to use the copula.
You can't say tá sé fear, you have to say is fear é, and you can't say tá dochtúir í, you have to say is dochtúir í. Mileata is just an adjective, and doesn't change the primary "noun is a noun" structure of the sentence.
You use an indefinite article to classify something, you use a definite article to identify something. The structure of the Irish copula depends on whether you are making a classification or an identification.
"She is a military doctor" is a classification copula. "It is the official newspaper" is an identification copula.