Just wanted to know if there were any K-9 dog handlers, specifically MP dog handlers. I've searched everywhere but cant find any info about the job.

What exactly do you want to know? I'm not one, but I worked closely with some and still keep in touch with a couple once in a while.  They were Air Force, but with K9 handlers (the leo ones anyway) you aren't just part of your own branch of service, but are part of the DoD in general.  As in where I worked with them, when I first got there, the kennel master was Army, most of the handlers were Air Force, and some were Navy.  Just sort of depends on who is available.    All of the training after Initial Entry Training/Basic whatever the name of the week is, is done at the same place with instructors from all branches.
There is a wide range of jobs that they do, from sniffing for bombs and drugs, to the attack training.  Most of the dogs are pretty much generalists, though some only have the temperament for a specific task.  The Army also has a few used by Enigneers for mine detecting, and not law enforcement.  From what I heard, it's a pretty tough school. LOTS of attention to detail, and learning how your dog acts, and it's attitudes and personality in general.

I helped the Marines train cats to detect land mines a few years back.

How long do they normally require you to have in service?
How often do you switch bases?
Do you get to stay with the dogs, afterwork?
Do you get any extra pay?
How long are the days/ weeks?

Quoted: How long do they normally require you to have in service? How often do you switch bases? Do you get to stay with the dogs, afterwork? Do you get any extra pay? How long are the days/ weeks?

Depends on the branch of service for most of these.

1: I think you can go straight into it, if you enloist as an MP/SF.
2: It depends on the service how often you'll PCS.  Usually a couple, three years.
3: Most bases (AF anyway) they are kenneled at the end of the day.  It was a treat for some of the handlers where I was deployed because they got to keep their dogs with them.
4: Not that I've seen on any pay table.
5: 24 hours a day, 7 days a week, 365 days a year.  It depends on your mission and location.  Road patrol at a stateside base could have you doing just a normal 8 hour shift five days a week.  Deployed could be 5 to 12 hours shifts (with a break so the dog doesn't overheat) for a month straight. I'm thinking VBIED sniffing here.