Yes you can absolutely rent a car in Dubai provided,
- You are on Visit Visa
- You have both local and International Licence
- You are more than 25 yr old
the condition is that you can only drive a rental car on International License, No personal or relatives cars'
On a side note, Pakistani International Driving license is accepted in all the countries of the world when visiting (not residing).
In some countries you can even rent a car on Local Pakistani license as well as its in English (Personal experience in Australia, USA and Europe).
I would suggest you to book your car online. Use sites such as Kayak.com or Expedia.com before going so you can save yourself hassle of bargaining and chatting with the staff at airport counters. If you visit in the peak season it might be sometimes difficult to get a car on the counter. Plus its always cheaper online. You need to have a credit card for renting a car, whether booking online or not.
Cheers