1
general::
An exceptionally zealous person, one who habitually takes on more tasks or works harder than others. For example, Bill is a real eager beaver, always volunteering to stay late. This expression became especially popular during World War II, applied to recruits anxious to impress their commanding officers by such behavior. [First half of 1900s]
American Heritage Idioms
2
general::
Phrase(s): eager beaver
someone who is very enthusiastic; someone who works very hard. • New volunteers are always eager beavers. • The young assistant gets to work very early. She’s a real eager beaver.
McGrawhill's American Idioms And Phrasal Verbs