Synonyms for Eager beaver:

n.

enthusiast, evangelist, aficionado, dynamo, fanatic, lover, supporter, man, go-getter, follower, devotee, fan, concern. eager beaver (noun)
live wire, busy bee, sharpie, sharpy.
industrious person (noun)
go-getter, live wire, busy bee, dynamo, sharpy.

Other synonyms:

go-getter. dynamo. Other relevant words:
enthusiast, fanatic, busy bee, dynamo, go-getter.