Take control of your metering. That means doing one of the following..
- using exposure lock
- understanding how matrix metering works on your camera in a variety of conditions or
- using spot metering
- using a light meter (ignore this for now - it's only here for completeness)
If doing 2, 3 or 4 you'll also need to learn how to use exposure compensation or manual mode. You don't need to use manual, it's just one option.
If you're spot metering then you'll probably want the whites of the dog's fur to read about +2 to appear white but retain detail, or the blacks to read about -3.
You just need to understand that if the camera's meter reads +3 then whatever you're pointing it at will be (nearly) pure white and if it reads -5 then it will be nearly totally black. Similarly I know that if I spot meter off the palm of my hand and it reads +1.3 then my exposure will be about right for most ordinary circumstances. Or you could meter off a grey card to set the exposure*
Exact results vary from camera to camera, and the colour you're pointing at can make a difference but the above is sufficient for most cases.
Note that on some cameras the spot metering always works off the centre; on others it wanders around when using a single focus point.
You should also learn to read a histogram. You can take a test shot and look at its histogram to work out whether your exposure is as you intended.
If you want to get really precise then an incident light meter is the way to go but again it's hardly necessary in this case.
Sorry, that's rather a lot of 'learn this' tips without any actual links to help you learn them. Google is your friend..
It's well worth reading, digesting and re-reading
@Pookeyhead 's tutorial
here
*You could use an 18% - or more likely 12% - grey card to set the exposure but make sure you get a properly calibrated one. Many grey cards are intended for setting white balance, not exposure, and some of them even suck at that.