Not sure how your pictures display perfectly. As popo says, it's 5:4 as opposed to the 4:3 of your FZ18.
I use my laptop's 15.4" widescreen (16:10) to edit and view photos as it's the closest to my photos (3:2, 15:10). I also have a secondary monitor which is 1280x1024 like yours and I use this as a second display to display my thumbnail grid in Adobe Lightroom.
Most screens nowadays are 16:10 and 16:9 is quickly becoming a new standard. To display your pictures perfectly, you will need to find a monitor that has the 4:3 ratio. Unfortunately, they are slowly being replaced although you should have no problems finding one. If you like the 5:4 of your old monitor, then you will need to look for another 1280x1024 display as I believe that's the only resolution offered at 5:4. Not sure why they keep it around, it's a very unusual aspect ratio.
A widescreen computer monitor, whether desktop or laptop, will not stretch the photo so it should look the same. The empty space or black borders around the picture will change as well as the size of the image but the actual aspect ratio of the image will not be stretched.