I did some Internet research and here are two substitutes if you get caught eggless.
1 teaspoon yeast
¼ cup warm water
1 ½ tablespoon water
1 ½ tablespoon oil
1 teaspoon baking powder
I've used both with mixed degrees of success in cake and quick bread recipes. Eggs provide leavening, so substitutes try to replace this feature. What they cannot do is replace the richness, colour, and flavor real eggs bring to baked products.
If you want to read more about our float cabin living on Powell Lake in British Columbia, go to www.PowellRiverBooks.com. There you will find a list of Wayne's books in the Coastal BC Stories series. Many include chapters about our cabin life, and right now the Kindle version of Up the Lake is FREE. -- Margy