First, let me fill in the gaps on your situation, based on the numbers you've given so far.
I estimate that your student loan balance (principal) is $21,600.
With the variable rate loan option that you've presented, the maximum interest rate you could be charged would be 11.5%, which would bring your monthly payment up to that $382 number you gave in the comments.
Your thoughts are correct about the advantage to paying this loan off sooner. If you are planning on paying off this loan sooner, the interest rate on the variable rate loan has less opportunity to climb.
One thing to be cautious of with the comparison, though: The $1200 difference between the two options is only valid if your rate does not increase. If the rate does increase, of course, the difference would be less, or it could even go the other way. So keep in mind that the $1200 savings is only a theoretical maximum; you won't actually see that much savings with the variable rate option.
Before making a decision, you need to find out more about the terms of this variable rate loan:
How often can your rate go up?
What is the loan rate based on?
I'm not as familiar with student loan variable rate loans, but there are other variable rate loans I am familiar with:
With a typical adjustable rate home mortgage, the rate is locked for a certain number of years (perhaps 5 years). After that, the bank might be allowed to raise the rate once every period of months (perhaps once every year). There will be a limit to how much the rate can rise on each increase (perhaps 1.0%), and there will be a maximum rate that could be charged over the life of the loan (perhaps 12%).
The interest rate on your mortgage can adjust up, inside of those parameters. (The actual formula used to adjust will be found in the fine print of your mortgage contract.) However, the bank knows that if they let your rate get too high above the current market rates, you will refinance to a different bank. So the mortgage is typically structured so that it will raise your rate somewhat, but it won't usually get too far above the market rate. If you knew ahead of time that you would have the house paid off in 5 years, or that you would be selling the house before the 5 years is over, you could confidently take the adjustable rate mortgage.
Credit cards, on the other hand, also typically have variable rates. These rates can change every month, but they are usually calculated on some formula determined ahead of time. For example, on my credit card, the interest rate is the published Prime Rate plus 13.65%. On my last statement, it said the rate was 17.15%. (Of course, because I pay my balance in full each month, I don't pay any interest. The rate could go up to 50%, for all I care.)
As I said, I don't know what determines the rate on your variable rate student loan option, and I don't know what the limits are. If it climbs up to 11.5%, that is obviously ridiculously high. I recommend that you try to pay off this student loan as soon as you possibly can; however, if you are not planning on paying off this student loan early, you need to try to determine how likely the rate is to climb if you want to pick the variable rate option.