Bonne fête des mères - petit-déjeuner as preferred spelling not per the Academie Française?

In this listening practice, it is stated that the preferred response is 'je prends mon petit-déjeuner' - that is, with the hyphen. I left the hyphen out. Checking on the Academie Francaise site dictionary, it does not appear to recognise the hyphenated form as being accepted at all, and refers to déjeuner as either the first or midday meal, noting that in common use 'un petit déjeuner' is used for 'a breakfast'. It does note that déjeuner itself is also a verb intransitive form, but does not list petit-déjeuner (or the informal petit-déj) as accepted. The Academie is obviously prescriptive generally and French for France, but even for dictionairies with a more descriptive approach, such as Larousse, the hyphenated form is not listed as a 'noun', and only as being used as a V.I. (familier) at times (ie Je petit-déjeuner and translated as meaning «je prends (son) petit déjeuner». On the other hand, le Robert dico en ligne, does denote the hyphenated form as a noun. At the least, I think it is incorrect in the lesson to suggest the preferred form should be hyphenated, as at best it seems to me an argument can be made that either is acceptable (although not if the Academie remains the ultimate reference for material on this website). Worth a look?