Product review (5 stars): Broan BPSF30-Charcoal Non-ducted Filters
They DO fit the Broan Allure QS1 series of range hoods.  These filter inserts are smaller than the external aluminum screens that come with the range hood because they are used BEHIND the aluminum screens as an addition.  They fit inside the frame of the aluminum screens and have clips to hold them there.  These filters came with very clear instructions on how to install them and it is very easy.  They work well, but keep in mind, this is non ducted, so all they can do is remove the particulate matter.  It definitely helps with grease and smoke while cooking.
I highly recommend this product and this seller ([....]).  Super fast delivery!!