I have 2 boys and a stair set up like you do. Where its about 10 steps then a platform, I have a railing with bars like you do and they will stick their head through but they never went through the railing! They never fell down the stairs and they have been going up & down them since they were 2 months old.

I don't think you need to worry about it too much. If the stairs were wood Id worry, they skid on wood, but with carpet they have plenty of traction.