Hi Terese I am from a Babington line as yet I not found your Eleanor in my tree but it is a large tree.But this hint might help you. Don't just stick to the spelling of Babington as Babbington, De Babington and even Bebington are the same family. And you have to remember that Dublin can be England as well as Ireland.
On one site I found Eleanor Bebington born 17th June 1798 Pontesbury, Shropshire, England. Father - John Bebington Mother - Mary.