RP will not be stamped in the passport if the staff doing it notices the valid RP of any other GCC country in the passport. If your friend is lucky, then it will be done, if they don't notice the other RP while stamping the RP in Qatar, as happened to two of my colleagues who had Duabi RPs in their passports.
In my case, my passport had to be sent to my previous employer in Dubai for RP cancellation after which Qatar RP was stamped. It was no problem for me to do so, as I am working for the Qatar branch of my orginal employer in Dubai