Since you state you hit a deer, I assume you will be making a first party claim to your insurance company, under your comprehensive coverage. Know your policy language first. It propbably states you are owed an "actual cash value" of the veh or a market value.
If you and the insurance company cannot agree on an amount, there is also probably an arbitration clause on first party claims in which you can envoke an arbitrator to determine the value. The down side for you is the cost of obtaining this as the insurance company will not pay for this, however if data is on your side, this can be a good way to get your $$ value. Also, the insurance company normally will go up in the offer to avoid this as it is very time consuming and a pain in the butt for a disagreement of only $2,000. Use this as your last resort.
To back up your value, get details on how they came up with theirs. You should then pull NADA, Edmunds, NADA Classic cars, and every web listing you can find, to show values of vehicles like yours. If you check the NADA classic values, the low retail is 4k on your car with high of 11k.
Throw every value and every car you can find on the net at them, along with every detail on your car. Do not give up on slamming them with information. Shoot them a high value and "settle" for the right value.
I was a manager in claims for over 10 years. As a general rule, all consumers think their veh's are worth more than they are, and every adjuster thinks they are worth less than they are. The difference is the one person is looking at it strictly from a transportation thing, and the owner has more at stake both $$ and emotionally.
That being said, you should be able to get 4-5k on this if you do the above, based on a quick search of values. If all fails, and you have some data that backs 5k, invoke the arbitration clause and see where that gets you..
Good Luck..
http://www3.nadaguides.com/Values/ValueCategoryReport.asp?UserID=5108065387E85&DID=37987&wSec=2&wPg=1207&CategoryId=12&MakeId=1115&VehicleId=36828&Year=1982&ColorId=