A perfect cross breed between Labrador Retriever and a Poodle is the Labradoodle. They were originally bred for this reason only, to make them low shedding. And the motto was well achieved. This dog doesn’t shed much and is a good choice for people with allergies. After they were bred, families couldn’t hold them for long from taking it to home.
Labrador is likable and desirable dog because they are smart and very social friendly. But yes choose wisely, their shedding depends on the type of fur. Also remember this, you need to spend ample amount of time with a dog before taking it to your home. You should know well whether that dog is good or bad for your allergies.