Do you write emu with a capital letter?

No, "emu" is not capitalized unless it's the first word of a sentence or part of a proper noun.

For example:

* Emus are large flightless birds. (The first word of the sentence, so it's capitalized)

* The Emu is Australia's national bird. (Proper noun)

* I saw an emu at the zoo. (Common noun, not capitalized)