I have Whirlpool Gold dishwasher that came with the pre-owned house.
When I open the door, there is a label and it says Energy Star with a number.

On the left side door edge, there is an area which appears that a sticker has fallen off. I believe this is where the model # was.

Is there another way I can figure out the model? Do you think it's in the back of the unit as well?

Thanks

Good that you found it. If the label is missing, there isn't a lot of chance finding the exact model number. However, any model would share parts with at least a few other models, and it's usually not difficult to find a correct replacement part. In addition, some plastic parts and most electric/electronic parts would have the part number stamped on them.