It looks like this will need to work on a PUSH basis from WooCommerce rather than being pulled from QuickFile. We already have an API for creating new sales invoices, clients and assigning payments, so I would imagine this data would be pushed in at the point of sale via our API.
Rather than develop complex integration for a long-tail of different systems we’re now looking at simply integrating with Zapier (see thread here). I already see that WooCommerce are connected to Zappier so this would act as a suitable bridge.