Check with your local glass company. They too often have plexi which they will cut to size for you. Go thick, leae the thin 1/8' stuff alone unless you are incorporating wooden or metal frame work to hold it. Then all you'll need to do is use a good solvent such as Weld-On#3 or in a pinch Tenax to cement it all together.
You could also use tempered glass, but that is something that the glass shop will have to assemble for you. They'll need to grind the edges smooth and use some of their wonderful glass binding cements to hold it all together.
Another resource is to use blown clear plastic, such as those found on cake pans...or a producer of plastic packaging might be able to make you a suitable sized and shaped piece...a domed cover.