I had not heard of Ann's connection to Richard Perring, although I did wonder what Henry was doing at Bathurst, where he died in 1875.
There is a possibility that Ann Pullen was born in 1827 at Studley, Warwickshire. Her father .. Henry & mother .. Jane
From your info. the last 2 children I listed are actually Richard Perring's children...plus Peter.
Just noticed that I have "Richard" here, on my file at home I have 'Richmond'
The 'Dale Park', sounds familiar, so I must have that somewher in my notes.
Have you actually seen the passenger list ?
Does it state her parents names, or where she was from ?