Raw eggs shouldn't be fed to dogs because of the salmonella risk.
To be honest, my opinion is that if your dog's diet is good enough then her coat should be very shiny without adding any supplements. My girl is on Hill's Science Plan and her coat is softer and shinier than any other boxer I've seen. It's expensive compared to Purina or Pedigree, but well worth it if you ask me. I buy the 15kg (33lb) bags, which last about 6 weeks.
A high-quality diet will go a long way toward a healthy coat - if you want to stick with kibble, the Whole Dog Journal list was just posted in another thread, and that's a good starting point for quality foods. Fish oil, as noted, is a good supplement, and raw eggs are as well. (The risk of a dog contracting salmonella is much lower than it is for humans, because of their physiology; it is not impossible, but not at all common. In fact, the only dog I know of with a confirmed case of salmonella contracted it from his kibble.)
First off Iams isnt a very good food! I would switch her.
Honey~~ Science Diet isnt that good of a food either.
I feed my girl Canidae ALS and her coat couldnt be shinier or softer!! She also gets canned sardines once a week(the ones in water, no salt) Our chow chow also gets fed this minus the fish and her shedding has almost completely stopped except for the normal twice a year! They had her on kibbles and bits(LMAO) and she shed all year round and looked very mangey!