Is there a way to customize output of Doxygen index.html (and latex equivalent)?

If you are looking for more customised cover pages in both LaTeX and html outputs, you might also want to play with the tags LATEX_HEADER and HTML_HEADER (and HTML_FOOTER).

This is answered by the first question in the Doxygen FAQ:

1. How to get information on the index page in HTML?

You should use the \mainpage command inside a comment block like this:

/*! \mainpage My Personal Index Page
 *
 * \section intro_sec Introduction
 *
 * This is the introduction.
 *
 * \section install_sec Installation
 *
 * \subsection step1 Step 1: Opening the box
 *  
 * etc...
 */