Believe it or not, this question was among the hardest to answer! There may be another interpretation, but I used the Cambridge Grammar of the English Language as my reference. On page 351 it states:
"i. a. dozens of spiders.....ii.a. a dozen spiders....The head in (i) is dozens....whereas in (ii) it is spiders...."
With that in mind, I am supposing that a dozen of /one dozen of can take either a singular or plural verb. However, if "spiders" is the head noun, I think that "eggs" is also the head noun.
*The Cambridge Grammar of the English Language, by Huddleston and Pullum. Cambridge University Press. 2002