One book that I learned to read with really stuck in my head because it was very similar to my own situation: A little sister who kept tagging around after her big sister trying to do everything she did and saying “Me too!” in every instance. I could swear the big sister was a brunette and the little sister was a blonde (as we were). My mom was trying to teach my big sister how to read, and even though I was only about 3 at the time, I wanted to learn right alongside her, because, well, “Me too!” I know there is a 1983 Mercer Meyer book along these same lines, but it has non-human protagonists and the older sibling is a brother. The book I’m looking for would have been published at least 10 years before that.