I think you can follow your travel plan, and then decide on the runtime whether your family need some rest,or not. The important thing that you need to consider is the travel time. From islamabad to Naran it usually takes around six hours but if you are with an infant, it's probably gonna take a couple of hours more. Because there are many things that you need to consider like the feeder, diaper changing etc. All these things take time and then also you may want to do some sightseeing, like maybe stop somewhere to take some pictures and things like that so it increases your travel time. I suggest whatever your travel estimates are, add two to three hours in each of those.
Secondly, in all the places that you are going to visit, the weather would be very pleasant for adults, but for infants, it would be cold (specially Naltar), and the kids have the tendency to catch cold quite quickly. So, I would suggest to take proper medicines for your kid with you. And also, if possible, take a nebulizer because if the kid catches cold and runny nose then nebulizer is usually the best way to help them breathe and sleep.
Third thing is that whenever you have to travel, start early morning, that gives you enough time and cushion to manage any delays during your travel, and you can reach your destination while the sun is still up.
And lastly, do take sunblock and mosquito repellent with you. You would need them quite much. Although season is not there for mosquitoes in Deosai, but still it's a good practice to have mospel handy.
Thanks