Doctor Adams is the author's father.
Richard Adams is the son of Evelyn Adams, who worked as a country doctor.
I can find no definitive quote from the author to confirm this was his intention: however the similarity in name, profession and locale make it seem extremely likely.
Some critics have taken the similarity as read. For instance in his essay "The Shrinking of the Epic Hero: Richard Adams' Watership Down and the Epic Tradition", Kenneth Ketchell of Louisiana State University says in a footnote:
The doctor is named Dr. Adams and, significantly, Richard Adams's father was a country doctor.
If university academics cannot source an explicit connection, it is possible that suppositions based on this strong circumstantial evidence is the best that we can do.