In general, yes, your dog will be safe in the back of your SUV. Legally, you are allowed to drive with your pet in the car. The Highway Code states that they must be properly restrained, must not be sitting in the front seats and should not be allowed to have their head out of the window. If a pet distracts you while driving and you get into a collision, your car and pet insurance may be invalidated if it is discovered to be down to your negligence that the pet was allowed to create such a distraction in the first place. You can face a fine of up to £5000 if your dog is not restrained properly. It is also recommended that you do not bring your dog in the car if they are very ill or injured, if they are newborn with an unhealed navel, or if they are not old enough to feed by themselves. It is important to try and acclimate your dog to the nature of a car before you set off as it can be quite daunting for your dog.