Chances are you've either bought a second hand TZ1 that came with its original battery and that no longer holds a charge, or you've fished your old TZ1 out from the back of a drawer and that needs a new battery. Whatever the reason, you're doing the right thing. The Panasonic DMC-TZ1 should be kept alive because its a good little camera. Replacement batteries are not hard to find, however, it most probably won't be Panasonic branded unless its fake, used or quite expensive.
The same applies to the charger if you want to buy one brand new. There's always used original chargers available on eBay, so that's always an option. The good news is, some of the after market batteries, specifically a selection of the German made replacements, are actually really good and hold a charge well.