offer letter if signed act as a confirmation of acceptance and should be sent back to the company in Qatar. But you should not resign until you receive your Qatari Visa.
Once you receive your Qatari Visa you should resign and give your tentative joining date to the company in Qatar.

Upon your arrival in Qatar , your company will provide you a formal labor contract which will be signed by you and the company's authorized signatory which will later be attested by the ministry of labor (will be done by HR).

I hope this information is helpful.

Cheers!!