You can not use non-standard video frame sizes in Premiere Elements, carrot. Sorry.
What is your source for video at this size? It seems to be full-screen off a computer monitor. If so -- and if you're using a screen capture program like Camtasia -- Hunt has some suggestions for working with that video in the Hints & Tips forum to the right of this forum.
But you'll certainly never be able to edit video at 1280x1024 in Premiere Elements.
Ya, I just did some extra research and it seems Premiere Pro has this capability. Fortunately, my school also has this available to me as well. Seems like a strange limitation to me.
What I like to do is capture and edit losslessly so I can use a really good H.264 encoder, like x264. The built in Mainconcept one isn't all that bad, but still doesn't compare to the quality x264 can produce. I previously used freeware applications for cutting/splicing but now I want to add more effects and filters to the video which was not previously available except in nonfree software.
Yes, PrPro will handle what you want to do. In CS5, you can even Import your footage into a Project, and then just drag it to the New icon (bottom of the Project Panel) and PrPro will create a New Sequence for you, to match that footage, so you do not even need to use Desktop Preset and manually customize the attributes to suit.
You can also have different Sequences (think mini-Projects) in a single Projects, that have different attributes.
PrPro can use many of the CODEC's installed on your system (a few more than PrE can), sot the x264 should work fine, though I have not tested that.