The question begs another question: Why?
Is your source footage really 1440 square pixels?
Any cam I know of that creates 1440 x 1080 uses anamorphic by design. You can then export to 1920 x 1080 square if you like to whatever you desitination is.
If you really have 1440 x 1080 sq pixel footage, you can create a custom seq preset any dim you like
Ah, but it is not coming from a camera. I am creating it from images. In fact the main purpose of creating this video is
so the projectionist can adjust zoom and focus to bring the projector back to optimal "standard" settings while the audience has something funny to watch. Sure, I could create it in DV 4:3 format, but my images are already sized for 1080 height (I made a similar video for adjusting the zoom/focus for widescreen, which is really 4:3 with the top and bottom offscreen since the projector doesn't do 16:9). It is an older projector before HD standards and 16:9, but is higher resolution than the typical 4:3 formats. Another reason I want to use higher resolution is because I previously made the video at 720 x 480 resolution and it looks much better in HD.
So the question remains - how do I set custom resolution with square pixels?
Aha! I figured it out. I need to set the "Editing Mode" dropdown to "Desktop" and then the frame size is no longer grayed out.