No, not from one computer to another, you'd have to copy the project files onto a server, NAS device, or external HDD and then load it on the MacMini. You cannot from your Air directly say hey PP on the MacMini let's do this unfortunately.
Now, one option would be network rendering. The thing about it is, both computers are required to have exactly the same project files which means it has to be hosted on a server or some sort of NAS device (costly, and won't benefit your setup that much), some frames get rendered on one, while frames get rendered on the other (both computers will be actively involved, so most likely you couldn't work on other projects).
PP does not support network rendering, so the file PP CC file would have to be imported to After Effects.