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Oh yes, I wasn’t suggesting that the OP simply copies information from WikiTree (or Ancestry for that matter!). But there is a page set up for one of the Dooley ancestors from Great Longstone. I’m suggesting that the OP contacts the individual listed as the owner of that page and asks for the information he has and his sources to see if there might be a connection.  In fact the church records are listed as a source for that page.

I am descended from Charles Titterton. He was my grandmother’s grandfather. Fanny was his niece, the daughter of his eldest brother John. John and Charles had 11 other brothers and sisters. Charles may have been the black sheep of the family, he certainly featured in the local courts a few times. Their father was John b1811, married to Elizabeth. John’s father was also called John b1782 married to Mary. That’s about as far back as I’ve gone.
Fanny’s brother Ernest married Maria McGowan who had a sad upbringing; she and her 9 siblings were orphaned and ended up in the workhouse as paupers.
Another point of interest is that Fanny’s first cousin William was the father of Sir Ernest Titterton, the nuclear physicist (associated with the atom bomb, Manhattan Project etc.).
As for the Dooleys, someone else on Ancestry has traced them back many generations. No Irish connection yet and it goes back to 1610 - still in Derbyshire. I’ve quickly added them to my tree but haven’t done my usual checks. You will need to check any available records to make sure the line is correct. However, that suggests that Samuel Dooley was born in Swadlincote but in 1829 not 1831 and married to Catherine. The Dooley line then goes back: Joseph, b.1797, William 1773, Edward 1742, Henry 1699, Henry 1658, William 1630, John b. 1 Jan 1610.
There’s a lot of conflicting information across the Titterton tree, I need to tidy up my version but I’m focused on my paternal line atm. Hope that’s helpful, regards Claire

I’m new to this group, so I know it’s a few years since your query. If it’s helpful, I have Fanny Dooley nee Titterton in my family tree. She was my first cousin, 3 times removed. Can’t help with the Dooley ancestors, only the Tittertons. As far back as I can see, to her grandfather (my 4th great grandfather) came from Staffordshire.