Yorkiemom1 offered some good advice. I totally agree with you that Pedigree isn't a great food and would not be anywhere near my first choice. But honestly, you don't want to potentially introduce GI upset into an already stressful situation for the pup like switching living environments and adjusting to a new home.
Whenever you decide to switch foods though, I definitely recommend Fromm. We currently feed the grain-free lamb & lentils kibble and some FreshPet which my two pups really enjoy! We have tried most of the premium dog foods out there and always come back to this brand...easy to find, great quality, and great price. Look into some of the Earthborn formulas too...Toki and Teddy both do well on this brand but I find we just can't get through the smallest bags that they have fast enough (wish I had a FoodSaver sometimes or more freezer space). Wellness Core is also a good option for a kibble that is easy to find in most major pet stores.
Good luck with your new pup! Keep us posted