How to stop up bathroom floor drain

Here's our problem.  Our daughter bathes in a removable baby tub that normally rests inside a full sized tub.  It would be a bit bulky to take with us on the trip, but we're thinking that if we could stop up the sink in the bathroom floor of the Pod, that would give her a couple of inches of water to splash around in and for us to bathe her.

So has anyone discovered an easy way to stop up the drain?  I'm not sure if I should just remove the grate and get a plug that will stick in.  My wife has found drain covers that lay flat, but I'm not sure how secure they will be.  Any ideas?

We only want to put a couple of inches of water in there for no more than a few minutes at a time.  Do your really think that will make it leak?  It's a shower after all.

By amazingly well, I mean: take a red solo cup, fill it with water to within 3/4" of the brim.  Take a square of Press n seal and cover the cup, sealing it only 1 1/2" down/around the neck (and cut off the rest).  You can turn the cup upside down, shake it, toss it in the air and catch it and it won't leak a drop.

And, yes, the shower pan itself is waterproof.  Putting a couple inches of water in it isn't going to cause any trouble.