Dogs naturally eat some plants as par tof there diet there is even debate if dogs should be considered carnivores or omnivores. The substances that are known to harm dogs are chocolate (Theobromine poisoning), onions, grapes and raisins,
some types of gum, certain sweeteners and Macadamia nuts. Thus I do not believe letting your dog eat broccoli and carrots will hurt your dog I often feed my dogs things other than there normal food and my dogs have never gotten sick. There should be no problem but if you want to be on the safe side ask your vet.