Well, first off I WISH I was even under 200 lbs (I'm 5'10", 32" inseam) so normally couldn't comment on size versus ability to handle bikes OTHER than I've taught new and experienced Motorcycle riders for about 5 years.
Fundamentally, if you want to handle it you can. I've seen women at barely 5' and maybe 110 lbs or (I'm guessing at the weight as I'd never dare ask them) ride a GoldWing GL1800. Now, they can put a foot down OK cause it has a low seat BUT the bike with fluids is over 900 pounds. So, Weight of the bike is NOT an issue.
I've seen people who are so short that they cannot get both feet down on a Honda 100cc trail bike (one of the smallest bikes we have for small people). The bike only has a kickstart so to start it they put it on the sidestand, mount the bike and can then kick it over, they can't reach otherwise. From a riding perspective they can barely touch both feet tippy toes to the ground. So, as long as you can do that you're OK.
I'm sure that the K1200GT with the lower seat would give you more than enough reach.
As a shorter rider (and I experience this on my some taller bikes), you have to be very careful of where you stop. If the road is sloping to the left, you'll need to stop with your right foot down. If a lot of heavy trucks have been through and created a couple of tire wells (deep impressions in the road), you must stop with the bike at the bottom of the well.
Good luck and enjoy the GT!