A typical consumer of the library takes the header file(s) and some binaries, and can develop her application on top of that. If the API documentation would be included in the header as well, that would be sufficient, no need to look into things created by Doxygen or anything else. However Doxygen documentation can also be produced from the header instead of the source, it just does not matter. So be nice and move all the API documentation to the header file(s).
A typical consumer of the library takes the header file(s) and some binaries, and can develop her application on top of that. If the API documentation would be included in the header as well, that would be sufficient, no need to look into things created by Doxygen or anything else. However Doxygen documentation can also be produced from the header instead of the source, it just does not matter. So be nice and move all the API documentation to the header file(s).