Flights to Gilgit are operational but they are not shown on PIA online portal because of frequent cancellations because of weather. There is only one flight daily from Isb to Gilgit and vice versa (depending on weather). You will have to book the flight by going to PIA Office.
You can't complete entire trip on private car because most of the places are only accessible by 4x4 Jeeps. I can give you a rough itinerary which you can refine with time.
Day 1: Flight from Isb to Gilgit, Stay in Gilgit
Hire a 4x4 Jeep for entire trip, it will be your memorable Jeep Safari.
Day 2: Gilgit to Astore (via Thalechi, Bunji More), Astore to Rama Valley (night stay)
Day 3: Visit Rama Lake. Back to Rama Valley and move to Deosai through Chilum. Camp at Bara Pani, Deosai National Park. (If you don't want to camp then you can continue to reach Skardu the same day).
Day 4: Reach Skardu (Stay for a little time at Sadpara Lake en route to Skardu), Visit Manthokha Waterfalls in Kharmang, Back to Skardu, night stay in hotel
Day 5: Skardu to Shigar, Night in Shigar
Day 6, Shigar to Khaplu, night in Khaplu
Day 7, Visit Khanqah Chaqchan, Machlu Village, Hushe Valley, Night stay in Hushe (Hushe is my personal favorite valley)
Day 8, Back from Hushe to Khaplu, Khaplu to Skardu, proceed to Shangri La Resorts for a night stay.
Day 9, Spend the day relaxing at Shangri La, Visit Upper Kachura Lake, spend another night at Shangri-La Or proceed to Gilgit and stay in night at PTDC Motel at Stak Nala (This will cut around 2-3 hours from long drive from Skardu to Gilgit).
Day 10, Reach Gilgit and proceed to Naltar via Nomal, night stay in Naltar
Day 11, Visit Naltar Lakes, and proceed to Aliabad, Hunza. You can visit Attabad Lake spillway the same day, return to Karimabad and stay at night at Duikar, Eagles Nest
Day 12, Visit Altit, Baltit Forts, Shop from Karimabad market and proceed to Gilgit for night stay.
Day 13, Catch flight back to Islamabad from Gilgit.
For entire trip, if you hire a 4x4 Jeep, (from Gilgit to Gilgit), it will cost you around 50K to 55K. Public Transport (like NATCO, Mashabrum Travels, Coasters) are a bad choice, only choose them if you are really tight on budget, otherwise always opt for flight or private car from Pindi to Gilgit.
