You could represent your superposition as (|00> + |01> + |10> + |11>). Adding one to this would turn it into (|01> + |10> + |11> + |00>). The carry is thrown away, like you thought, but the result is still a superposition of all four values between 0 and 3. Thus, your plus-one operator doesn't change the superposition. But it would have if we started with, say, (|00> - |01> + |10> - |11>).
Slashdot Mirror
You could represent your superposition as (|00> + |01> + |10> + |11>). Adding one to this would turn it into (|01> + |10> + |11> + |00>). The carry is thrown away, like you thought, but the result is still a superposition of all four values between 0 and 3. Thus, your plus-one operator doesn't change the superposition. But it would have if we started with, say, (|00> - |01> + |10> - |11>).