According to that Canadian site:

" A coin was struck that was equal to the value of one male beaver pelt – it was known as a « buck »."

Significantly, no shred of evidence is given to show why this would have been the case. Or even that it was the case.

Supposedly it was in the 1600s - but Oxford dates the "dollar" sense only to 1856.

Of course, beavers do have buck teeth and Bucky Beaver used to advertise Ipana toothpaste. Brusha brusha brusha!