I'm editing 24p 1920x1080 Uncompressed 10 bit 4:2:2 on Final Cut Pro and I need to finish on HDCAM. If I brought a Quicktime Movie to a Post House would they be able to transfer that to HDCAM or would I need to convert the footage into 1440x1080 interlaced first? I'd prefer to master to HDCAM SR but the delivery requirements don't allow for this.

Don't convert to 1440x1080 interlaced.

They will likely feed a 1920x1080 signal over HD-SDI into the deck (and the deck will internally do the conversion to 1440x1080). Check what editing system they have and what Quicktime codec they support/prefer. Also check what file system your external drive has to be in.

Your best bet is probably to communicate with them, and let them know what your delivery requirements are.