This is the way we do the laundry around here. Well at least the girls. For their clothes I decided against a conventional dresser and opted instead for a system of bins in a shelf unit. I chose this specifically for this purpose.
When I pull their clothes from the dryer I tell Emy it's time to get out her bins and play our sorting game. She gets hers one at a time and I grab Elly's. We line them up in the same order so it is easier for her to find the right bin.
Then I sit on the couch and fold the clothes handing them to her to put in the correct bin. ( I never said they get put away neatly, particularly when Emy tries to use her teeth to carry them)
Afterward is the push back to the closet. Here Elly's trying to help but is caught on a box of diapers.
And we are done all the clothes are in and the bins are back in the closet.
She loves it, the laundry gets folded and put away lickity split. Happy kiddo, happy mommy.