azzi, no Employment Contract is required for submitting the work visa application. Even the Job offer has nothing to do with the visa.
Normal practice is signing the Job Offer which serves as a mutual agreement and acceptance of the offered terms and conditions, and which outlines the main points of the future Employment Contract. Once the work visa is issued and you are in Qatar, they will let you sign the Contract which will be a part of requirements for issuing your Residence permit.
Normally you won't get any contract signed, until you are in Qatar. Contract should contain at very least your work visa number, which you still don’t even have. So your priority now is getting a work visa.