Registration book, road tax receipt, driver's license, CNIC, and just to be on the safe side, 3rd party insurance (can be easily made in few hundred rupees from civic center). If the car ins't in your name, then an authority letter from the owner (along with their CNIC copy) mentioning that you're allowed to use their car.
Check all lubricants, brakes, battery, tires, and radiator.
Take a pair of extra hose pipes, and a bar of any cheap soap in a small container (like a baby milk formula container OR a zip lock bag). Dip the soap in water and tightly seal it. This will come in handy just in case, god forbid, you have a leak in the radiator because of any reason. The soap would be soft enough to fill the crack and allow you some respite to take the car to a mechanic.
Road conditions are generally good. Your intended route is alright except that M3 is the way to go from Abdul Hakim to Lahore as was mentioned earlier. M4 will take you to Pindi Bhattian via Faisalabad and it's mostly used by Islamabad bound traffic.
Why would you want to stay the night at Multan which is only about 3-3.5 hours short of Lahore? A better place to break the journey--if you want to break it anyway--is Sukkur in my opinion, so that you only have to drive a maximum of 8 hours on both days.
Otherwise, if you leave Karachi at 4AM, you will reach Hyderabad at sunrise, the traffic would still be less on N5 and you can easily take your 1st (longer) break at Moro. You are a better judge of your car and driving style, but here's my proposed itinerary:
Leave Karachi at 4AM
Reach Hala around 7AM and have breakfast
Leave Hala at 7:30AM
Reach Moro at 9AM, take a tea and washroom break, Royal Taj and Super Madina restaurants are better option.
Leave Moro at 9:30AM
Reach Sukkur at 12noon. Take a snacks/early lunch break
Get your fuel tank refilled to full capacity, as there is no fuel station and service area on M5 just as yet.
Leave Sukkur/N-5, take M5 at 1PM
Reach Multan around 5PM, take a break for tea and snacks, but for that I believe you have to exit M5 as there isn't any service area operational as yet. Shah Shams Tabrez Interchange OR Vihari Road Interchange are closeby.
Leave Multan at 5:30PM through M4
Take M3 from Abdul Hakim (you don't have to worry as there're clear signs available for Lahore and Islamabad)
Reach Lahore around 8:45/9PM
You can easily save an hour if you are judicious in your rests and driving.
I hope it helps. Regards