when covering female vocals, should i sing the same notes but in a lower octave or try to match her octave?

Answer 1

Whichever your voice sounds better doing...
Alternatively, if the vocalist's original melody is a little too high to be comfortable for you, take it down a few keys to one that suits your own range.

Answer 2

like someone said whatever sounds best
instead of singing the same with her why not try half an octave below or an octave

Answer 3

there's no much rules or must dos in music. so which sound the best is the best.