Doerr is derived from the German verb dorren, the "o" having an umlaut which when anglicized becomes "oe".
Dorren (with umlaut) means to dry, desiccate, dehydrate, or kiln dry.
A Doerrer or Dorrer (with umlaut over the "o") was, thus, a person who had the occupation of drying something, quite likely, fruit, grain, or perhaps a firer of clay or pottery.
It seems highly probable that your ancestors at some point had this occupation, from whence their family name was derived.
This analysis was made free of charge by someone who has studied German, has lived in Germany, and has studied the origin of names and whoknows how to read a German dictionary and who has ties way back when to Dorr's and Dorrsam's (Dried seeds).
Just remember, free advice is what it is worth, but, in this case, it is a very costly donation of time, effort and logic. Good luck!