Hi Nicholas,
For exporting tiles from these services you will need to authenticate with an arcgisonline account.
This guide topic Access the ArcGIS platform—ArcGIS Runtime SDK for Qt | ArcGIS for Developers should give you some idea of how to go about authenticating your app. You probably want to look at the AuthenticationManager section. The API reference for that type (AuthenticationManager Class | ArcGIS for Developers ) also has some useful information.
Basically, you need to respond to the request for a token with some credentials - using the AuthenticationManager (singleton) with an AuthenticationView qml component will give you a sign in experience.
Does that make sense?
One question I had is whether this is a one time export (e.g. to prepare the data) or if this is something you would like your app to do ever time it runs?
I hope that helps,
Luke