Please do not leave too early in the morning due to early morning mist but just after Fajar should be ideal
I am not sure if you can make the trip in two days back from Lahore.
Reaching Sadiqabad from Lahore in one day is not an issue. Its the second part of the journey, from Sadiqabad to Karachi that will take you a lot longer.
The roads are under construction hence traffic delays and detours from one side of the road to the other to face oncoming traffic so reducing the chance of passing safely. I recommend you stay on the N5 due to constant traffic 24 hours and services throughout in case of an emergency. Its a well traveled rout and very safe.
Secondly, since the days will be shorter in December you will have less daylight hours for traveling.
I think that if you shoot for Hyderabad from Sadiqabad it may be doable in a single day.
But quite frankly, it will all depend on your ability to get around traffic, and the traffic conditions that day plus your stamina as to just how long you guys can travel without stopping.
I think three hours may be possible on the first part of the journey but after that you will need a rest of 3 to 5 minutes just to stretch your legs every one and a half hour in order to reduce the chance of fatigue which can really put you at risk while driving.
And finally, do not travel during sunset because you will be facing the sun just before maghrib which is quite dangerous and stressful driving with traffic coming your way.
The rest, stop regularly to drink water. Stop for tea at a chai dhaba along the highway. Just remember its not a race, you are going on a pleasure trip so slow down, make some stops for lunch, the occasional tea stop and enjoy the journey.
In the event you need to stop for lunch or dinner, or even for a night stay near along the way from Lahore, I highly recommend you stop at a beautiful Charpai Hotel in Uch Sharif. You may remember the place from the photos on my thread.
There you will meet a person by the name of Arsalan. His mobile number is 0342 798 3262. Give him a call when you reach Bahawalpur or even a day in advance. Give him my name and he will be more than happy to host you. He is a wonderful person and I have stopped there many times, even a month back on my recent trip from Islamabad where we drove back by car and shipped our bikes to Karachi from Pindi.
Have a safe journey, take plenty of pics and have fun.
Sulaiman