Qatar is almost as low risk for Rabies as the UK, I really wouldn't panic. The two most dangerous complications of a dog bite (and only if it is a big bite, little nips don't count) are crush injury (requires xray) although children have a far lower risk of damage and infection from the saliva.
There hasn't been a case of Rabies recorded here for a long time. HMC have a protocol for animal bites but there has to be a puncture wound. Are you sure this is why they won't do it? If they say it's not necessary, please don't worry