I don't see any major problems of your email up to here. Only this sentence is too direct "Seems like you are doing a lot of work by yourself, unless you don't mind or are happy with it."  From her email, I couldn't sense that she was uncomfortable with your proposal . Once she said she was okay, I would stop responding to her email about how she felt about taking more tasks in the project.

What I would concentrate in following communications is how to develop the outline of project deliverables. Of course, let her know my appreciation to her efforts too.