Maria/Dinah McDermott - born 1840 Dublin

[NigelG]

Can I ask for some help/advice please?

I can only find definite mention of my Gx3 Grandmother on the 1871 census where she is recorded as Maria Biddle, Widow, Laundress - age 31 - born Dublin, Ireland.

Confusingly, on her daughter's birth certificate (my Gx2 Grandmother Annie Biddle) in 1866, she is recorded as Dinah Biddle nee McDermott (birth is registered at the same address recorded on the 1871 Census - 7 Upper Beckwith St, Birkenhead).

So, I'm looking for a Maria (possible Mary) or Dinah McDermott born Dublin c1840 & family that possibly all moved to Liverpool/Birkenhead between 1840 & 1860 (her first child Clive (?) was born in Birkenhead in 1860).

Do any"ship manifests", "passenger" or "arrival" lists exist for Irish immigrants to the Liverpool/Birkenhead area that may help me narrow down my search??

This is my major brickwall & I'm really struggling with this. Help!