This is a somewhat complicated question. On the surface, it doesn't seem fair that you have to pay more for insurance if you have to use it. Underneath that, the insurance company has to be very careful about customers who file too many claims, or have a tendency to cause injury or damage through carelessness. If the incident in question was not your fault, your premiums should not increase, but there are some mitigating questions that need to be looked at.
If you have a history of filing insurance claims, even when the incident is not your fault, then your insurance company is likely to increase your rates. If you file too many claims against a policy, the insurance company can also choose to cancel or not renew your policy. Similarly, some types of claims may carry designated premium increases, such as dog attacks or damage caused by a natural disaster in an area which is prone to that particular event.
Dog bites actually fall into a special group of insurance claims, and have the potential to cause your premiums to go up or bet the policy completely cancelled, depending on the wording of your policy. For example, many insurance companies are reluctant to provide coverage for homeowners who raise bull dogs. If your insurance company is one of those, and you own a bull dog that bites someone, the claim will be denied, and you may stand a chance of losing your coverage completely, or simply face higher premiums.
All insurance companies have different procedures and rules. The best way to find out whether your premium will go up after a claim is to contact your insurance company and discuss the topic directly. If it makes you feel more at ease, ask the question hypothetically, as though you were considering purchasing a policy from the company, not as a customer who already has a policy.