Thank you for taking the time to reach out to us here on the Community page. I'm here to help share information about projects.
As of now, adding these fields fields (Start Date, Expected completion date, and others) isn't available in QuickBooks Online (QBO). However, I'll take note with this and pass along the suggestions here on my end. In this way, our product developers/engineers will take a look and work on with this.
For additional reference about projects, you can read this article: Projects FAQs.