You have an awesome camera in the Lumix. The sensor in it is eight times as big as that in a point and shoot, which will yield good pictures in general, and better pictures in low light (once you learn how to work it, and maybe pick up a couple of specialzed lenses). It's also relatively small. If I were you I'd stick with that and just work on your photography skills. That's really what's going to improve your pictures the most anyway, regardless of the camera you use! There is a Mirrorless thread on the Photography Board if you want to see what it (and cameras like it, which include the Olympus PEN and the Sony NEX, whose sensor is even a little bigger) can do.
For those who want to buy Mirrorless, do your research into what they're all about and what features they have. There are quite a few to choose from now, and more will be coming out. They are evolving. (And some older models have come down in price but are still very usable.) Also hold them in your hands to see if it's a comfortable fit and if the dials and such feel intuitive. Most mirrorless cameras are not exactly carry-in-your-pocket like point and shoot cameras are, although with the smallest lens and minimal other accessories, you could do that. But once you see the nice pics you're getting you'll probably want other lenses and some accessories so you can have even more fun with it! What's nice is that it's something you can grow with that way if you want to, or not. But either way, a fairly small bag should suffice.
There are some different schools of thought on the memory cards. Some people don't like to keep all their eggs in one basket, so to speak, so they have and use multiple cards in case one gets lost or malfunctions, etc. Memory cards are a lot cheaper than they used to be, so it's easier than ever to have several. I like to buy the ones that say Extreme III, or something to that effect, on them, since they can write faster and therefore your camera is ready for the next shot sooner. I'd probably keep older cards primarily as spares. Also, always use your best settings unless you absolutely need to squeeze in a few more shots or something - don't let cards stand in your way of getting "best" pictures.