It will depend upon your state's laws and also your insurance company's rating system. In some states Comprehensive claims cannot cause your rates to rise so if you live in such a state your premiums should not go up due to you making a claim for the damage the deer caused to your vehicle.
If state laws do not say whether or not an auto insurance company can raise rates after a Comprehensive claim then it is up to the rating system of your insurance company and their guidelines. Typically since you are not at fault a claim for damage sustained due to hitting a deer will not raise your rates, however if you have already had claims then this claim adding to the amount of claims you have made in total with your insurer may cause your premiums to go up.
Ultimately, you will need to talk to your insurance company. Remember, even if your insurance company says your insurance rates will increase, you will need to weigh that against driving around in a damaged vehicle (or not being able to drive at all due to a disabled vehicle).
You can get a quote for auto insurance Ontario or anywhere else in Canada and the United States here to compare your rates.