Flipping from his stomach to his back

In the last week or two our baby has begun flipping from his back to his stomach.  At first it was troublesome, because he would do it in the middle of the night and scream and scream until we came in and flipped him back.  Sometimes we'd find him with an arm or a leg stuck through the sides of the crib, but they say that bumpers are dangerous until your child can turn themselves from their stomach to back.  Today for the first time (that we've observed) he flipped from his stomach to his back!  The problem is, in the process of turning himself over and over he's getting out of his funky farm playmate (pictured below).  When he's in the mood for it the mat is great entertainment for him and allows us to take care of chores around the apartment within earshot, but now that he's rolling out of it we can't use it as a makeshift babysitter anymore.


It was very exciting to see him get himself onto his back for the first time, but it marks a new era in the mobility of our child.  He still needs more tummy time to work on the strength of his arms, but the next step is probably crawling.  He is able to move himself forward a little on his stomach, pushing his face into the ground in the process, but isn't at the point where he can cover any real distance.  But he gets so excited and smiles so much when he does it, I'm sure because we get so excited, that I don't think I have much time left before I really have to baby-proof this apartment.  Until this point the only thing I've done is put safety latches on the cabinets under the sink, and that's to prevent our cats from getting into the trash more than anything.  I haven't even put all the faceplates on all the electrical sockets from when we first moved in and painted about a year and a half ago.