From the fic itself:
A burly young Dwarf, not even seventy, was stacking wood for the braziers that would warm the night-watchmen. His bright red hair was pulled back into workman’s braids, his short beard thick on his cheeks and tied into two small braids that stuck out either side of his chin. His face was set and pale. “Glóin’s son,” he said in surprise.
“Aye,” said Frerin. “Did you forget him?”
(ch2)
And
Mizim smiled at him, and threaded two golden beads onto the short tufting braids of his beard. “You look very handsome,” she told him.
“For a troll,” Gimrís added cheerfully.
“Gimrís!” Mizim snapped. Her daughter rolled her eyes.
(Ch3)
OH AND AND AND ALSOOOO
“Oh,” Frodo said, and he looked puzzled for a moment. “It seems so strange. I mean, sixty is passing middle-age for a Hobbit, and yet it’s only young to a Dwarf.”
Gimli smiled at him. “Very young. Your uncle met me a few years after the Quest, and no doubt he thought me a very raw and callous youth. Why, I could barely braid my beard properly, and it stuck out in two tufts! Terribly embarrassing. I’m glad none here saw it!”
(Ch11)
LASTLYYYYY
From Follow the Leader:
He bows his head, and then he looks up once more, a sad smile tugging at the corner of his mouth. He reaches up and unbinds his short beard before taking out his belt-knife and cutting three locks from it. Hair already dusts the feet of the three statues: some more will not make an appreciable difference. His bright red hair joins the others, to moulder away along with the bones of the honoured dead.
“You bloody sods,” he says, and then he laughs softly. The echoes laugh back: a thousand Gimlis are laughing at him. “My beard is long enough to braid now,” he says to the solemn face of Kíli. “No more tufts. How jealous you would be!”
SO yeah – the answer is yes, he had an awkward tufty time of it for a while.
Aw Yiss 