How can I get a free visa which.allows me to stay...

Please kindly note that according to the data provided to us in your inquiry, there is no such thing as a free visa to stay in the State of Qatar, especially if it adopts the residence law with an explanation of the procedures for obtaining a visa, so it is possible to apply for a free visa
It should be noted that after reviewing your inquiry and legal scrutiny we would like to inform you that about the free visa, this is just by name and that there is no existence for it by reality and therefore referring to the law of residency for expatriates in the state
Article 21:
The employer, the Competent Authorities, and the Ministry of Labor and Social Affairs may agree to transfer the Foreign National laborer to another employer before the time limit in the contract has been reached or after five years of working for the employer if the contract did not specify a time period.
The Foreign National laborer may, with authorization from the Competent Authorities and the Ministry of Labor and Social Affairs, transfer to another employer in the event of the Recruiter’s death or dissolution of the body corporate for any reason.
In all cases, the employer serving as the Recruiter shall not have his legal rights, or the contract between him and Foreign National, violated, in accordance with the referenced Labor Law.
The aforementioned article organized the cases of which the employee can transfer to another company as follow:
• With an approval from the employer (Whatever the contract is)
• After completing five years on unfixed term contract
• The end of the fixed term contract
• The death of the employer
** Therefore, returning to the question you can move because the employer agrees, and you must apply in this regard to the professional entities accompanied by a reference to the employer's approval
Therefore, in the event of submission of resignation may result in depriving you from entering the country once again for a year