I just checked
Infiniti Homepage
Unlike US where it automatically comes with 3 year 36000 miles warranty, looks like you have to buy warranty from the dealer when you purchase your car in Dubai. Take a look at this chart
Infiniti: Service Contracts
Do you have (did you buy) any warranty on your car? Also, even if you didn't, I don't see them charging a lot of money just to change your belt.
Keep us posted.