In the next release of doxygen (1.8.3) I plan to introduce a new configuration option USE_MDFILE_AS_MAINPAGE
which can be used to specify a markdown page that is to be used as the main page.
Then you can configure doxygen as follows:
INPUT = README.md other_sources
USE_MDFILE_AS_MAINPAGE = README.md
and it will work regardless of page's headings.