The Canary Islands are spanish islands so the rules are the same i would think.
My local vet told me that after 6 months of age i needed to register the dog with my local town hall(relevent department).
Also the dog must have rabies jabs at 6months.
Also the dog must be on a lead at all times and kept on a muzzle.
This last muzzle rule on my island (Lanzarote) is not kept to by anyone and police turn a blind eye.
No dogs on beaches is a bummer and gets a 50(approx) euro fine but finding early hour quite deserted beaches is a piece of cake for me .
Finally (just remembered this one)dangerous dog owners themselves have to undergo a psycology test to see if they are mentally stable to own such a dog.( i am told this is easy to pass)
I would check the local vet 1st where ever you will be living, as most towns might have slighty different local rules.
Hope this helps ;)