Man, I have no clue how it was worked out in Oman. But here the things are different.

In worst case, if you met an accident, how the police in Qatar will give you the report to rectify ? or if the accident is in your mistake, how the third party claim your insurance ?

If you are in over speed, how the police put penalty in your name plate ?

where will you change you istimera ?

It is unbelievable that your car was in oman for two years.

when you enter in Qatar, they didn't ask you how long your stay in Qatar to take the car with you ? and no limitation ?

It is uncommon to see the other countries name plate in Qatar. Even if the case they may in for temporary .

Instead you should have sold your car there and buy another in Doha.