I am a Military Working Dog handler and I agree with what most of the members here posted about K9. In the Army, most K9 handlers are 31B's (Military Police) and most of the time, we have to re-enlist to get the school. I had to re-enlist. Though, if a unit really needs dog handlers, then sometimes re-enlisting is not necessary. There have been a few guys in my current unit who were just "given" the school, did not have to re-enlist at all.
I know SF and Rangers have dogs.....Engineers also have dogs, but I hear as an Engineer, it is very difficult to become a dog handler, there are only so many Engineer dog handlers.
As far as making K9 it's own MOS, they've been talking about it for years....they've been talking making K9 a 31K MOS. But I think if that were to ever happen, it would be way after I get out/retire.