Hello dianalmark,
Welcome to the Community. QuickBooks is the go-to program for business owners looking to streamline their payroll and get ahead with their work. I'll be happy to provide more info so you're on the right track.
When it comes to your employees submitting their expenses in QuickBooks, you'll have to have them manually add time to your payroll. This can be achieved using the Time tracking features in QuickBooks Online Essentials and QBO Plus. This can also be done while using QuickBooks Time. To learn more about these features I recommend checking out this article here that provides in-depth information.
Feel free to ask questions as you go through the article. I'll be a message away in case you need anything else. Otherwise, I wish you a great rest of the week.