Henley and Shiplake are, according to Google Maps, only 2.6 miles away, so it's safe to say that Rachel is born in the same area.

I did a quick search, and as you said, Oxfordshire is not very well covered. If I were you, I would contact the Oxfordshire Family History Society. I think they carry out searches for you for a small fee, or you could try playing around on their website to see if you can find anything.