One D-cell would be a lower voltage. 3AA would give a longer run time than 3AAA, and 3C or 3D would give even more. To go down to a 1D would probably require boosting the voltage with a regulator. a 3AA > 1D adapter would work fine though.
Remember, one AAA, AA, C, or D, all have the same voltage, just different capacities. Changing the voltage can mean that you'll need to change the circuitry around as well, though this isn't always the case. If this is an unregulated light then most likely 1D would run it very very dull. You'd be better off with a 3AA to 1D adapter in that case...or just a 3AA light.
Seeing as it's 3AAA if you want more capacity you could try going with lithiums or rechargables.