Is there a restriction on Doha, Qatar for going outside due to the pandemic?

Can I freely leave hotel and go for shopping, let's say? Is there any rule I must aware of?

No curfew but some businesses are cut down to some extent e.g. https://www.gco.gov.qa/en/top-news/phase-4-statement/ (mirror):

• Continuing normal working hours at malls while keeping capacity to 50%, and opening food courts in malls with a capacity of 30%. Allowing children to enter malls.
• Allowing the increase in restaurants capacity starting with 30%, according to the procedures which will be set by the Ministry of Commerce and Industry.