Thank you all very much for looking for me.
Everything points to this being my Emma, except the ages given.
She was born in 1884, so on the passenger list she would have been 34 / 35, not the 30 as stated.
On the death notice in 1921, she would have been 36 / 37 - not 32 as stated.
I wonder if it isn't my Emma at all, but just a coincidence that this Emma was from Dudley as well.
Would the New Zealand death certificate give her parents names etc?
If not, I will have to purchase her marriage cert to find out for sure.
Thanks again for your help,
Darin.