I don't know if Qt provides an API for that. Here's the OS X specific information.
On OS X, it depends whether it's a GUI app or unix level support libraries. For a GUI app, it's the standard practice to have all the read-only data shared by all users inside the app bundle itself. Typically you have
YourApp.app/
YourApp.app/Contents
YourApp.app/Contents/MacOS
YourApp.app/Contents/MacOS/YouApp .... this is the binary
YourApp.app/Contents/Resources/ .... here are all the shared data
The GUI presents the directory YourApp.app
as the application itself, so that you can copy/move it around without any problem.
If that's not possible, it's recommended to use the subdirectory of
/Library/Application Support/name_of_your_app/
for data shared among users.
It's a bad idea to have a mutable, shared data among users on a machine; in general it's impossible due to the access restrictions. Note that a standard user might not have, and in fact usually does not have an administrative right to write into a shared location.
For mutable data specific to a user, use
~/Library/Application Support/name_of_your_app/
See this Apple guideline for more info.