This seems to have become a very controversial subject in recent years. It used to be quite widely believed that feeding a dog a high protein diet (such as a raw food diet) could make it more hyper/nervous/aggressive etc. and that if you had a dog that was anxious or too lively or aggressive you should feed a lower protein diet. Similarly, it was thought to be beneficial to put elderly dogs, or those with kidney problems, on a low protein/higher carbohydrate diet.
More recent studies have come up with evidence that it's not the protein levels (%) in a dog's diet that influence behaviour or health, but the quality of the protein. Good quality protein from a good source is much better for dogs than poor quality protein from poor sources.
My 2 are raw fed, so have a high protein diet, and personally I think that suits their health and hasn't caused any behavioural problems. William is 8 years old and I did some online research a while ago after somebody suggested he should be on a senior food. I'm confident that his high protein raw diet suits him and have no plans to change it.
If Ruby is thriving on Harringtons then I would suggest keeping her on it
I would worry about feeding something like Bakers that has lots of colours, additives and fillers. Personally I think those sort of things are more likely to cause behavioural problems.