I'm here to help get you pointed in the right direction for integrations with QuickBooks Desktop.
We can't suggest what application is best for you and your business. For third-party applications to help with the integration of project management software and QuickBooks, you can check out our Intuit Solutions Marketplace at https://desktop.apps.com/home. You can find tons of apps that are compatible and designed to work with QuickBooks Desktop.
Also, there's a community dedicated to developers and configuring of applications with QuickBooks. This site contains resources for software development, as well as the ability to ask fellow developers questions. You can find additional information about this at the following link: Intuit Developer.