Hi Xeeshan
If u can delay a little then i will advise to travel on 13-20 April or 20-27 April. Neelum Valley will be full of spring colors and views are very beautiful.
It is still one of the areas where cost is very low. IF u will use public transport then rocket bus will take u all the way from MZF to Kel in just 300,400 Rs.
Food and hotel cost is very cheap in Neelum Valley so not an issue at all unless u want to stay in AJK Tourism or Valley Trackers. Your per day meal and stay cost can be as low as 800-1000. Kel to Toubutt will be jeep ride and way opens somewhere in early April so that is another advantage of going there in mid- late April.
Day 1: Lhr-Muzaffarabad, visit Pir Chinasi if u reach in time
Day 2: Take rocket and drop at Sharda. Explore the spring there
Day 3: Kel, visit Arang Kel and explore the area
Day 4: Visit Taobutt and back to Kel.
Day 5: Back to Kundal Shahi and a side visit to Kutton. Back to MZF
Day 6: Back to Lahore