Cynthia: maybe this will help
Here is some info for you
Should work, but will need to be a very sturdy basket to support the weight
Here is a Hometalk project using apple baskets. You could do this with laundry baskets as well. Just make sure you have a Heavy duty hamper for this to work:
There are a couple laundry basket planter ideas here:
https://www.hometalk.com/search/posts?filter=laundry%20basket%20planter Here are some ideas!
Do you have a picture of what you are looking for? A laundry basket seems pretty big to hang filled with plants. Or do you upcycle the basket somehow to be a plant hanger?