Hello jasonoyi318,
Yes, QuickBooks Self-Employed allows you to calculate your estimated taxes and pay it within the program. You have two options when paying the taxes; mail or online.
If you want to do it online, you still need to set up your EFTPS account. After that, you can freely pay your taxes. You can use this article for more information: Pay Federal Estimated Quarterly Taxes.
You'll also want to take note of the payment due dates through the IRS website.
Let us know if you have additional queries so we can further assist you. Have a great day!