Where do sheep go to get their hair cut?
Why this joke works
A Sheep Needs a Haircut
A barber shop becomes a baa-baa shop when the sound associated with sheep replaces the beginning of barber. Haircuts connect the shop to the woolly customer, so the answer fits both the setting and the animal. Say the two baas with a steady rhythm rather than a long bleat. The recognizable shape of barber shop should remain audible underneath the sheep sounds.
A closer look
The accent changes the match
The sound match depends somewhat on accent. Speakers who pronounce the r in barber strongly may need the written baa-baa spelling to make the substitution obvious. That is a delivery difference, not a reason to imitate another person's accent. A short sheep sound followed immediately by shop usually preserves the intended connection without an elaborate animal voice.
Fact behind the joke
A real wool-cutting tool
Sheep shearing uses a cutting handpiece with a comb and cutter. The comb selected affects how much wool remains, and some cover combs deliberately leave a protective layer of fleece. The joke borrows the idea of a human haircut for a real animal-care task.