Why not set it in a plastic lid of a storage container? Keep it simple.

Photo of Pul on back of changing pad.
 

I put Pul on the back of the changing pads I make. In the photo you can see the quilt lines. I use a walking foot.
I like your idea of quilting first and then adding the Pul to insure the pinholes don't cause leaks.

I used PUL on the back of bibs--keeps drooly baby shirts dry! It's good to work with but kinda pricey that I wouldn't use it for under the fish tank. I was going to suggest a flannel-backed tablecloth --couple layers together but the vinyl placemat is a good idea, too. That's what I have under the food/water bowls for my kitty but it's on vinyl flooring. I'd be really careful of anything that there is actual wood underneath as any moisture that collects will ruin that. It could collect under the mat you are proposing. Do you have something like a trivet that the bowl/tank could sit up off the tabletop that moisture can evaporate? Look in the dept with flower pots for plastic ones? Just so there is a bit of space between the tank and the wood surface.

How about one of those pads they use for folks that are incontinent...they come in different sizes ,,, and are washable if you don't like the white or off white then cover it with your choice of fabric... they can be cut down to size.. Many older people use these in their recliners or lift chairs.. I think Walmart has them, most drugstores, or they can be ordered on line.. they are waterproof.... I like the idea of the flannel backed tablecloths too Marc's has them for $1.99 sometimes or stores like Big Lots or Ollies...

I bought PUL from Fabric.com. They had some cute prints at least for what I needed; you can't pin but I used the
wonder clips and they worked fine. I made drawstring bags for wet bathing suits! The cording was put in so it could also be used as a backpack.

From an old fish keeper--put down a piece of vinyl, etc, and put your decorative pad on top. But splashes and leaks will STILL happen. And from an old fish lover--get your betta out of that fish prison and into a larger tank. Despite now these lovely fish are displayed for sale and the inadequate containers sold by pet stores .they deserve better treatment. You can keep a cat or dog alive in a crate but I bet you wouldn't do it. Please, please use your computer to find reputable betta care.

I would use a piece of rubber sheeting. That is what is used for bed wetting. It feels 'flannelly' on both sides so it would be gentle to your table top and you just throw it into the washer. If you want to make it pretty, just stitch a piece of PUL to the top. Neither fabric frays, so you could just stitch around the edges. (PUL is a treated fabric that feels like it has a soft laminate on one side. You often find it in the baby fabrics, Joanns carries a line called Babyville.) And, whenever I work with anything laminate or vinyl or thick, I use clips.