How would you say "hat selling dog" in Japanese?

[ronCYA]

You guys know what this is in reference to :P I have a few ideas but they're all just stitched together logically, not linguistically:

帽子売りの犬 or 帽子売り犬

帽子行商の犬 or 帽子行商犬

Any experts/natives know what would be a correct way?

[Keith_APP]

Cool :-)

It should be 帽子を売る犬 though

[ronCYA]

Oh okay thanks! Would this be "a dog selling a hat" though? 帽子を売る男 would seem to mean "a man selling a hat".