NIK Software also makes local color adjustments easy, using control points and Viveza sliders.
One advantage in using a flash is that it would produce catch lights in the dog's eyes.
For close up work (like this apparently is) I will use my flash in bounce mode (with the flash tube pointing straight up) modified with my Joe Demb Flash Diffuser Pro. I tilt the FlipIt portion of the flash at a 45 or more degree angle towards the subject. That way, the only light that strikes the subject is that which is bounced off the FlipIt potion. I have increased the size of the FlipIt. The light is quite soft and doesn't impact the subject to any great degree. However, it does add some light to the shadows caused by the back light and as mentioned above produces catch lights.
If I am shooting from a distance, I point the flash directly toward the subject. I will often use a thin tissue (like a Kleenex) in front of the flash tube to diffuse the light. If the flash has a diffusing panel, I will use that. A -1 or -2 EV flash exposure compensation keeps the flash from making the subject look unnatural.
BTW, I always have a hotshoe flash with me when I am shooting outdoors. I really like the Canon 420EX Speedlite for this use because it is the smallest and lightest full size hotshoe flash Canon has ever produced in the EX range of flashes. This flash fits easily in the pocket of my photo vest or in the front pocket of a small camera bag. It is also small enough that it isn't inconvenient to carry mounted on my camera. I have used the 270EX II but, that little flash doesn't have the power for fill from a distance and cannot effectively be used bounced outdoors.
Despite the fact that it doesn't allow for manual flash, the 420EX does have HSS capability which is a necessity when shooting outdoors. I like the Canon EX series of Speedlites because after selecting HSS (it is selected on the flash unit for the 420EX) you can forget about it. It will revert to regular sync when the shutter speed falls below the maximum camera sync speed and then automatically revert to HSS if the shutter speed is faster than the max sync speed. I will often use my camera in manual mode with the flash in auto TTL...
I have several other flashes (600EX RT, 550EX, and others) but, I like the little 420EX so much that I recently purchased a second copy (at less than $40 USD) from eBay as a backup...