How long does Quick Start take to transfer data?

To expand on Joseph’s answer, the actual data transfer will only take a few minutes. But it does not include your music and apps. These must be downloaded from the iTunes & App Stores. That can take considerable time, and depends on your connection speed and how much media content you have. With my iPhone, for example, syncing my 10,000 tracks and 290 apps takes about 5 hours. That’s over a 100 mbps Wi-Fi connection.

Hello mtmuggs,

Thank you for using Apple Support Communities.

There isn't a specified time for Quick Time to transfer data. It will depend on multiple variables, like connection method, signal strength and signal interference, to name just a few. You can take a look at the following support article to transfer data from an old iOS device to a new device where the only time frame mentioned says "Quick Start occupies both devices, so make sure that you choose a time when you won't need to use your current device for several minutes."

Use Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Best regards.