Boleh lah! I see so many Muslim men and ladies posting on this FB site https://www.facebook.com/MalaysianDogsDeserveBetter
telling people about themselves keeping dogs and some even so kind as to drive injured stray dogs knocked down by cars on the highway to seek vet treatment and footing the bill themselves. They said Islam permits rearing dogs, it is just that many Muslims are ignorant about it.

I salute her compassion.

Rabies is usually spread to humans by a bite, less often the virus is spread by the infected animal licking you around the mouth,
nose, eyes, or an open skin wound.

FYI, Rabies in domesticated dogs are no longer common.
Rabies is usually transmitted through the bite of an infected animal like a raccoon
skunks, coyotes, foxes, bats, stray cats, dogs, ferrets and other wildlife.