No. It was a completely original idea of mine. I never saw any Doctor Who episodes until I was 14.
I also had time portals that randomly appeared. One took me to another world by way of my house's double-window doors and the other linked my age to time on Earth, not in the world that I had landed in (which is good, because one Earth year equals 100 of the other world's years).
I was an extremely creative child. I had no siblings and didn't have any friends who lived close enough for me to visit their house every day, so my imagination went wild.