You need to go to the insurance company of the other person's car which as you state is QIIC since the police has given a decision in your favour. Go to them with your car as they may be taking photos of the damages for their files. You should also take with you the police report. Once you are there, they may ask you if you have any workshop of your choice for carrying out the repairs. If you don't, the insurance company will recommend you to a workshop with which they have agreement. But this choice is not given by all insurance companies. Please note once you put the vehicle in the workshop, the people there will give you an approximate time for completion of the work. Keep following up with them as workshops rarely meet their commitment on completion of the job. Also, if you go for genuine replacements of damaged parts, the common rule is that the insurance company will charge you 50% of the cost of original parts. However, if you opt to go go non-original spares (commonly known as Tejari), you will not need to pay a single Dirham from your pocket.
I write only when I know and can guide properly, Otherwise, I don't write for the sake of writing ........ my pal!