Residence Permit is NOT a type of visa. This is a permission to live in Qatar on the status of resident (not citizen)… Working visa is a permission to work in Qatar. In your case, you will have an RP under working visa, or they call it Residence Working visa, which means you have an RP with the permission to work. RP could be issued under family visa as well. (Residence Family visa)
First, working visa is issued for the certain nationality and gender, not for the particular parson. Then, this working visa is applied to the particular person with issued RP.