If you haven't already bought superoir/EZ drummer you might want to consider some of the drum refills such as the Ryan Green Alt Drums here
, as well as the relatively new BFD core refill
The above refills are just as good as EZ drummer with the added bonus of them being compatible with reason. There's also a tutorial series on hooking up an ekit with reason here
Also plenty of results on google
This might also help with mapping you kit http://midipipe.en.softonic.com/mac
If you still prefer EZ/superior drummer however, you can record the audio directly into reason from the standalone app using soundflower, jack or something similar to route the individual channels. (that is if midi sequncing of the drums isn't a concern for you)
As of midi connections, the axiom isn't necessary if you have a midi to usb cable.