you can ask them for whatever you want, it's up to you what to ask…
but if you mean, whether or not the work visa can be issued while you are in Qatar, the answer is yes. work visa can be issued while you are in qatar. in this case you will have a copy of it. then you exit the country and enter again on this work visa.. although again, i cannot see the reason for exiting, unless it's not related to the work visa..