Sir, the gentleman is travelling with family, I would always recommend him the safest route instead of the shortest.
And as far short is concerned, the route you mentioned is 1457 KM from Karachi till Islamabad Motorway M2 toll plaza and the route I and other members suggested is 1459 KM as per google maps. Please see the attached google map references. Even if the route you mentioned is the shortest, the difference is distance is not very significant. Saving a few kilometers and a few liters of petrol is not worth the hectic drive and safety risk.
Route: N5 till Lodhran, Khanewal expressway, Mian Channu, TobaTek Singh, Gojra, M2 till Islamabad
Route (Jazz82 mentioned): Uch Sharif,Alipur, Muzaffargarh, Attarahazari, jhang n Gojra motorway