Update: Quickbooks Desktop 2017 now allows you to set up scheduled reports. Full instructions are available here.
Quickbooks does not have a native automated report function, which means syncing your inventory is a very simple manual process.
Open the Reports module and select "Define a New Report." For filters, there should only be two: [UPC, Qty]. This will run and save the report to your computer. Run this report for each store if you have multiple locations.
Meanwhile, download and install Dropbox onto your computer. Create a new folder entitled "Locally" and share the folder with dropbox@locally.com.
When Quickbooks generates your reports, find them and drag them into this Dropbox folder so that they overwrite the previous day's inventory reports. The file name must stay the same each day. That's it!