Can I have a log of emailed transactions such as invoices and payment receipts?

Yes, you can, @1106506.

We have an Audit Log Tool that lets you see the changes made by a user and who made them. By viewing the Audit Log, you can keep track of all activity in your account.

To access, here's how:

1. Go to the Gear icon at the top.
2. Select Audit Log.
3. Click the Filter button.
4. Choose the appropriate User, Date, or Events filter to narrow the results.
5. Under the Events section, click the radio button beside Show only these events, then check the box beside Transactions.
6. Click Apply.

From there, it'll display all the transactions made on the account based on the filtered date. Then, find the invoice you've sent and click the View hyperlink to review the status of the email. 

To learn more about this tool, see this article: Use the audit log in QuickBooks Online.

Please let me know if you have any other questions. I'm here to lend a hand. Have a good day.