From Wiktionary, the free dictionary
Blend of egg + pregnancy
eggnancy (uncountable)
- (informal, rare) The condition of being eggnant.
2002 June 29, CreativeAlchemy, “Re: Help!!! ASAP!!!!”, in rec.pets.birds[1] (Usenet), message-ID <20020629072544.26817.00001732@mb-da.aol.com>:Baths are very healthy during "eggnancy" and also while the hen is sitting on the nest after she's laid.