The noun 'deer' is a common noun, a Word for any deer of any kind.
A proper noun is the name of a specific person, place, thing, or a title; for example:
- "Dr. Deer" (Dr. James C. Kroll), TV show on the Sportsman Channel
- Deer Valley Resort, Park City, UT
- Deer Street, Salinas, CA or Deer Street, Portsmouth, NH
- Deer Park 100% Natural Spring Water
- "The Deer Hunter", 1978 movie with Robert DiNero, Christopher Walken