If you have UK passport, you can get Visa on arrival in Qatar.
A work visa is surrounded by problems such as availabilty to the sponsor, not usually a problem for engineers, but intensely so when someone is caught up in some controversy, e.g. no visas available for Philipina maids apparently now.

What is most likely happening here is that someone wants to appoint you for a job. This must be passed through many departments and approved by all. This takes time, in my case some six months to join a Government Ministry a lot of years ago.
When it comes down to it you will be asked to jump through hoops of getting attested copies of certificates, police clearance certs. etc. Until this happens you are really just waiting. Maybe the job is there, maybe not.
Don't give up the day job until confirmation comes!