Currently there is no way to setup a dynamic date in the email body of the invoice template.
You can create recurring transactions by going to the Gear icon > Recurring transactions which can be used to generate invoices at set dates, which will show the invoice date, however the email body and message on invoice are default and would have to be manually edited before sending.
If you'd like to leave feedback for this feature request you can do this by going to the Gear > Feedback and we may be able to implement this in a future update!
Hi async128, there is unfortunately still no feature for this in QuickBooks Online, we'd recommend leaving feedback for this (Cog > Feedback) as this is based on customer-demand, so the more input we can get, the better. :)