Yes, you can. Though most car rental companies in the UAE prefer to rent out to driving license holders which are atleast 6 months old. You can still rent a car with a new driving license
However, please note that the insurance terms may differ for those with driving licenses less than 6 months old. For instance, the insurance coverage is only 90%, which means that incase of any accident or damage due to your fault (Dubai Police Report required). You will be liable to pay the excess amount and 10% of the amount the insurance company quotes.
Please ascertain the terms from the car rental company you are booking with and read the car rental agreement carefully before signing.