Bird and plane are both ndege. You basically always know which one is meant though because the difference between animate birds and inanimate planes is usually marked on some other part of the sentence, like this:
Ndege kubwa (inaruka) = A big plane (flies) Ndege kubwa (zinaruka) = Big planes (fly)
Ndege mkubwa (anaruka) = A big bird (flies) Ndege wakubwa (wanaruka) = Big birds (fly)
And what's wrong with the word aeroplane? American words and spellings are not compulsory on the internet. If it were asking you to type the English, it should accept both, but if it said "airplane" I could just as well say "I never use that word!" but obviously I know what it means.