Assalam o Alikum, first of all I wish and pray for the well being of yours and others around you. It is almost two years that I'm at Quetta and traveling by road from / to Quetta. It has been with my family , without family on my personal car as well as public transport. Alhamdullilah I did not find it insecure rather I prefer to travel by road. You can travel on following route from Lahore to Quetta:-
Lahore - Sargodha - Mianwali - Chashma - DI Khan - Daraban - Zhob - Quetta.
I started early morning around 0400 hrs from Sohawa, hit Talagang , Mianwali and than followed the route and Alhamdullilah offered Asr prayers at my home at Quetta.Regards and AllahHafiz