Welcome on-board CappuccinoGirl! (coincidentally my favourite coffee)
As Mark says, the GX1, like all compact system cameras with big sensors, won't be able to match your FZ with a single lens. That's the tradeoff you'll need to make: big sensor with great quality, but shorter zooms, or big zoom, but with smaller sensor and poorer quality.
I'm currently wrapping-up my GX1 review and have very much enjoyed using it. Do also consider the others at the bottom of this page:
http://www.cameralabs.com/buyers_guide/ ... DSLR.shtml