Good to hear you are out of your comfort zone.
Yes there's no problem of having baby with you, just take along proper items of her with you, and warm clothes ofcourse.
Weather will be pleasant in day with colder nights.
I suggest you to please call and confirm from any local hotel in Naran for Babusar route condition before leaving, if Babusar is block then you will have come back to Mansehra to take KKH for Gilgit/Hunza.
From where you are starting your trip by the way?