Peter Davison (in-universe)

Peter Davison was an actor (COMIC: The Girl Who Loved Doctor Who, WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors) who portrayed "Doctor Who" in Doctor Who. He was considered by the Twelfth Doctor to be one of the greatest actors on Earth. (WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors)

The Doctor once saved him from a Krynoid. He thought that something seemed familiar about him. (COMIC: The Girl Who Loved Doctor Who) He was brought together, along with many other actors who portrayed "Doctor Who", for a special breakfast in "London's glittering West End". The Twelfth Doctor considered making an appearance, to "see what these fictions [were] like." (WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors)

Information from invalid sources
In the 1999 television story The Kidnappers, Peter Davison played a version of himself who was kidnapped by two obsessed fanboys (David Walliams and Mark Gatiss), who act inappropiately towards Davison.

In NOTVALID: The Five(ish) Doctors Reboot, Peter Davison portrays himself again.

Other matters
Evidently, "Peter Davison" was, in all instances, intended to be an in-universe version of the real Peter Davison, who portrayed the Fifth Doctor. Although he was not given a clear in-universe illustration during the narrative of WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors or COMIC: The Girl Who Loved Doctor Who, the end of the webcast included a screen featuring photographs of each Doctor who would be present at the event, in-costume as "the Doctor". If taken as an in-universe representation of Davison, this qualifies as the only in-universe illustration of the character outside of parodies and other invalid stories.

All Creatures Great and Small and Button Moon exist in the DWU. In the real world, Peter Davison played one of the main characters in the former, and performed, alongside his former-wife Sandra Dickinson, the theme song for the latter.