Apple Watch cellular cross country

No.

https://www.apple.com/legal/warranty/products/warranty-us.html

IMPORTANT RESTRICTION.

Apple may restrict warranty service for hardware products to the country where Apple or its Authorized Distributors originally sold the device.

Here are the cellular carriers that support the Apple Watch. Make sure your carrier is on the list.

https://www.apple.com/watch/cellular/

Assuming your carrier supports the Apple Watch, it should work. There are 2 cellular radios, and both Qatar and India use the same radio (The other radio is for Canada, U.S., Mexico and Puerto Rico radio)

You should cross check the Apple Watch Feature Availability, as some countries restrict some features, and the software loaded on that Apple Watch will not provide the feature, even if it is allowed in your country.

https://www.apple.com/watchos/feature-availability/

Be aware that the warranty will be for Qatar, and you will have to return to Qatar if you need any warranty service.