Almost, it could mean 'the dog for the cat', as a phrase out of context.
This reminds me of a children's song, you have it in English too in several versions I think. In Swedish it's Bä bä vita lamm - "Baa, baa, white sheep". Wikipedia article here: https://sv.wikipedia.org/wiki/B%C3%A4,_b%C3%A4,_vita_lamm
So in this song, there's talk about how everyone in the family gets new clothes:
Helgdagsrock åt far och söndagskjol åt mor
och två par strumpor åt lille, lille bror.
(roughly: 'holiday coat for father and Sunday skirt for mother and two pairs of socks for little little brother')
In the song it's obvious that the clothes are for the members of the family. But people will often jokingly say that this is the song "about the family that ate clothes" because the other interpretation is also possible. :D