Thanks for reaching out to us here. QuickBooks Online gives you the option to connect your Gmail to your QuickBooks account. However, the option to connect Outlook to your QuickBooks isn't available at this time.
I can see how being able to send invoices from your Outlook would be beneficial for you and your company. I recommend Leaving feedback by heading to the Gear icon and selecting the Feedback option. These comments are viewed and considered by our developers as they create new features and updates for QuickBooks. In addition, If you're interested in knowing how to connect your Gmail to your QuickBooks, here are a few helpful articles I recommend looking at.