Mushkpuri is not a difficult trek and can be done in a day. From Nathiagali governor's house, its about 3 hours trek. All you would need is a day pack with water and some snacks.
The cheapest place to collect the hiking gear is Landa near railway station. You can find sleeping bags, rucksacks and shoes there. Do search Sunday market for the stuff.
If you end up buying sleeping bag from Landa, make sure it is polyester filled and is washed/drycleaned prior to use.
For new equipment the options in RWP/ISB are Gown house at Muree road (expensive), there is one shop, can't recall the name at Beverly centre in Blue area and a shop called Summit I think in G-9 or G-10.
Better and cheaper gear, sleeping bags and tents can be purchased from Higher in Lahore. they do home delivery via courier service too.