The usual advice is to start putting some of the new premium food in with the old food at each meal time, and over a few days, gradually increase the ratio of the new food to the old food. The hope is a slow transition lessens stomach upset.
ZoE was exactly 6 weeks to the day when I got her & barely had any teeth through her gums and had great difficulty eating the kibble that came with her. Her vet had me get Royal Canin Mini Babydog and she loved it & was able to eat the tiny pieces. She transitioned to puppy food at about 10 weeks. If Snoopy is already able to eat his kibble, that is great