Dicalcium Phosphate, Maltodextrins, Natural Flavoring, Microcrystalline Cellulose, Whey, Montmorillonite, Non-Fat Dry Milk, Brewer'S Yeast, Lecithin, Taurine, Choline Bitartrate, Hydrogenated Cottonseed Oil, Magnesium Stearate, Ferrous Sulfate, Stearic Acid, Ascorbic Acid (Vitamin C), Vegetable Oil, Vitamin E Supplement, Vitamin A Palmitate, Zinc Sulfate, Niacin, Silica Aerogel, Vitamin D 3 (Cholecalciferol), Biotin, Riboflavin, Cyanocobalamin, D-Pantothenic Acid, Manganese Sulfate, Pyrodoxine Hydrochloride, Thiamine Mononitrate, Copper Carbonate, Cobalt Carbonate, Potassium Iodide, Folic Acid, Sodium Selenite And Vitamin K (Menadione).
Some of those are not in the food I feed. I do find it interesting that they list Taurine as an ingredient. That is also in Red Bull. If anyone wants a little history lesson, Taurine is named after Taurus as it was first isolated in an Ox. It is also a major part of bile.
The food should be more than enough for the puppy as long as it is a quality food.
There are many dogs that were never given puppy vitamins or even dog vitamins in their life and lived long lives. Elizabeth is 18 months and doing great. I changed her food from IAM's Large Breed Puppy to Nature's Variety Large Breed Puppy and when they stop producing that and only made the Large Breed Puppy in the Raw Boost I switched to that. Gus is somewhere between 5 and 9 years old and was found as a stray and afraid of everything. Needless to say, I highly doubt he was fed a premium diet as he went from about 110 to 140 under my care. He was too skinny when I saw and eventually got him. I forget what they had him on but it was better than the "BIG" names. I moved him to Nature's Variety Raw Boost and he is doing fine as well.
For many centuries dogs have been pets in one form or another and yet they didn't have vitamins. Look at the origins of the pet food industry.