You will be assimilated.
Firstly, what are your comp settings?
Is the 1080 clip HDV, or HDTV? HDTV will have a Square PAR to begin with, but HDV (1080 flavor) will not.
What are your composition settings?
Are you using the Render Queue, or the Export function (you should be using the former).
What settings are you using in the Render Queue?
What is the desired frame size of your final destination? Frame Rate? Codec?
The easiest way to bring footage into a comp is to just drag your footage into the new composition icon at the bottom of the Project window. This creates a composition with exactly the same settings as your footage. If you haven't already started a comp you can just drag the footage directly into the Composition Panel or the Timeline Panel.
This is the simplest workflow and it means that your Composition can be rendered directly to the same codec that was used to capture the footage so that your NLE can handle the footage without rendering.
The other option is to create a new square pixel HD comp by using one of the Presets that most closely matches your footage (ie., 720 or 1080) then just drop your footage in that comp. Just make sure that the frame rates match.
While I'm talking about frame rates you MUST make sure that you know what frame rate was used for the original footage. If you have progressive footage it may or may not be interlaced with pulldown added. The list of possibilities is far too great to go into here. Brian Maffitt had a great slide last year at NAB that showed how simple HD was to understand. The ugly truth is that we all thought that life would be easier when we all started doing HD, but in fact there are literally thousands of combinations of frame rates, frame size, pixel aspect ratio, compression, data rate, and codec combinations. It's now more critical than ever that you completely understand how the HD footage was shot and captured and how the footage is to be used. My last HD project was delivered in 30i, 24p, 720, 1080 and NTSC DV Widescreen. The ASTC has defined at least 18 standard HD formats for use in North America. Who knows how many more there are when you throw in the rest of the world.
Well, you're not telling AE what it shall do, that's why. as Steve said, first make sure to interpret your footage correctly. AE should do this automatically 90% of the time, but you never know. Then use the correct composition settings. If the footage interpretation is correct, it is no problem to correctly place anamorphic 1440x1080 HDV files into a square pixel HD comp and the otehr way around, a square HD clip will fit correctly in an anamorphic comp, if interpreted the right way. Once you have that worked out, you can add your stuff to the render queue where you now need to take care of the correct field settings and choose a suitable media format. Just follow the links Steve provided and it wil lall become clear.