Also, a slightly different angle might have helped. If you had moved to the right a bit, more of the rim light might have been shown...
What I might have done is to use fill-flash a bit to open up the shadows of the dogs coat just a touch. A -1 or -2 stop fill might have given some modeling to the dog. However, the color balance might have been off since the flash would have been 5500-6000K and much more blue in color than the sunlight. I always carry a pair of gels that I can modify my flash color balance with. One is a green which I use when using flash in a predominantly fluorescent lit scene and an amber gel which I use when the scene is lit predominantly with tungsten or with a reddish glow of the sun...
When the flash is balanced somewhere near the ambient light, it is easy to modify the entire image in post processing...