Connect with few travel agencies to get an idea (whatever way you are going to travel, then build your own itenary..
You will find lot of travel agencies via FB ads..
Dont give everyone a budget, just ask for quotes, share only with few.
Yeah, looks OK. Try and squeeze in a night on one of the house boats on Dal for the sake of experiencing it. Also, do visit the Shankaracharya temple too since its next to Dal lake. Quite serene / peaceful - overlooking the city and the lake.