I wouldn't recommend doing this over WiFi!! Do it via ethernet. You'd need a USB to Ethernet adapter for the MacBook Air. You also can't just use a regular Ethernet cable if you don't use something like a hub or switch. You'd need an Ethernet cross over cable.
You'd have to specify an IP address of the iMac and then do the same for the MBA. Once done, you could open up your iMac's hard drive from your MacBook Air in the Finder after you enable File Sharing in Settings. It will show up as a network drive on your MacBook Air. Open iMovie for the first time and then immediately quit it. It will create a new iMovie library file in your Movies folder. Drag this to your iMac's hard drive and put it in a folder. You could then open iMovie and there's an option to switch libraries in the File menu and then navigate to your iMac's hard drive and find the library file.
The next question I have is what kind of drive is in the iMac? If it's not an SSD then you're not going to have a good time. But saying that, editing iMovie over the network isn't going to be fun either.
External SSDs are relatively cheap and you could pick a Crucial drive for about £60 ($70) which would be infinitely better than my suggestion above. You would plug that into your MacBook Air via USB and, open iMovie, let it create the library, immediately quit it, then go to your Movies folder and move over all the iMovie stuff to the new external SSD. The next time you open iMovie you could switch to the library on your external SSD via the open another library from the File menu.
You might also find that buying an Ethernet cross over cable (or cross over adapters) aren't cost effective. Plus with an external hard drive, you can move it more easily between machines. Even slower SSDs are in the 500MB/s speeds where as with gigabit Ethernet that's build in, you're looking at 100MB/s perhaps a little over.