Welcome to YT and congrats on the new baby!
I use a child's play pen.
Summer Infant Surround Sound Play Yard : Target
My pup was a year old when I got him, and I never had an issue with it. He never was able to escape, but it also depends on how you train them. I've mentioned this in another thread, and if you teach your puppy to wait at the door and never put him/her in our out of the pen over the railing, you won't be teaching him/her that it's ok to jump over. They're smart and can figure out they can get out, but they don't need you to encourage them. Good luck!