Room Time?

I'm attempting to try to teach Karsyn to play a little more independently. Several of my friends have their kids do something they call "room time" where they play for a specified period of time in their rooms. I am trying to talk Karsyn into doing this and telling her how "fun" it will be. I tried to start with 15 minutes, but within 2 minutes she was hanging over the baby gate I put up and screaming for me to come in and play with her. I've even dropped our dog Josie in the room with her to see if that would help. Still, no luck...

What suggestions do y'all have? How did you teach your kids to play independently? Help!!!!