I guess your tour is too long (considering honeymoon).. However if u have no issue of time, then you can follow following itinerary (assuming short travel time daily):
Day 1 : LHR to Balakot (around 9 hours travel) following murree route
Day 2 : Balakot to Naran, you can visit shogran in between..
Day 3 : Stay in Naran (visit saif ul mulook)
Day 4 : Naran to Fairy Meadows with short stays at Babusar Top and Lulusar lake in way (your car can go till Raikot Bridge, after that you have to hire jeep and then trek for around 3 hours to reach Fairy Meadows)
Day 5 : Stay in Fairy Meadows (explore its beauty)
Day 6 : Fairy Meadows to Hunza
Day 7 : Stay in Hunza (visit forts, eagle nest)
Day 8 : Hunza to Khunjerab (visit attabad lake, passu cones and sost in way), come back and stay in Hunza or stay at Sost (depend upon how much time you stay at Khujerab pass)
Day 9 : You can stay in Hunza or drive back to Naran
Day 10 : Naran to Lahore
In September, it will not be peak season so you will get the rooms at reasonable rates like around Rs. 3,500 per day in decent hotels..
No idea about fuel cost (maybe around 10,000 to 15,000).
