When I entered my tunic in the County Fair I had similar dog-hair concerns. So I washed and dried it, then laid it out flat on my bed and... took a roll of 3" or so wide Celophane tape.
Cut off about 8" or so and wound it around my hand, sticky-side out.
Then I systematically pressed and released the sticky surface all over the surface of my tunic, up and down, over, then down and up.
When the sticky got all stuck, I just cut a new piece, threw the old one away, wrapped the new tape around my hand again and resumed pressing the sticky surface against my tunic.
Then I flipped the tunic over and repeated the procedure. Therefore all the outside of my garment got stickied.
Then I blocked it and entered it in the Fair. BLUE RIBBON!! And no comments on the presence of dog hairs.
Hope this helps,