My first thought was yes, it will trip the breaker. Quick review of Ohms law in my head to confirm it will draw roughly twice the current.
What muddies the question is the somewhat arbitrary choice of 1000w for the toaster. And thus the resulting borderline calculation on the trip curve of a 15A breaker. It might take long enough (5 minutes?) for a particular 15A breaker to trip that the answer to the question might as well be 'no', because by that time something has gone up in flames.
Why not make it a 1500W toaster oven? Then the answer is a pretty clear 'yes' and you can separate the seasoned electricians from the not so seasoned.
Why is the problem such an issue? You did the math, and you say, it will trip, PERIOD.
Some will say, the current will drop in half because the voltage goes up. That is the guys we are looking for to understand why they may be thinking that.
I cannot say this any clearer on why we have this problem in the first place. It is to remind you about resistance and when its a fixed value and when you can change it, like in a dual voltage motor.