My advice is to record PRECISELY what you ordinarily do, make some of that (maybe as cupcakes?)
and to then substitute in ONE EGG for one of the equivalents of egg in that recipe. (For us, that is a tub of babyfood fruit, usually, so the conversion was quite straightforward. I just omitted the tub of baby food and put in an egg.)
HTH.
As long as you record EVERYTHING very carefully so that the doc knows what s/he's offering your child and how much egg is in it, everything should be good.
Good luck!!