Your options are as follows.
1) AxeFX --- > PA
2) AxeFX --- > Powered FRFR Speaker ---> Mic ----> PA
3) AxeFX --- > Powered FRFR Speaker
--- > PA
4) AxeFX ---- > power amp ----> Speaker Cabinet ----> Mic ---> PA
5) AxeFX ---- > Power Amp ----> Speaker Cabinet
----- > PA
Now in option 1 you rely completely on the sound guy for foldback. Now I have found that in many venues, even when you get a soundcheck, the foldback tends to be reasonably average (not ALWAYS the case, just to often) So that's something to think about. The sound guy will love this option though... reduced stage noise... no excess amp noise so he can make a balanced mix!
Option 2 allows you to just set all your levels and tones in the AxeFX with the inbuilt impulses for cab sim and not worry about the front of house volume being slightly different in the patches (so some patches are louder/quieter than they are supposed to be due to the gain structure of the desks preamps).
Option 3 means you get your own on stage volume and the sound guy gets a copy of the signal and doesn't have to worry about micing up your cab and extra stage noise. As long as the desk doesn't have crap mic preamps, and that your patches don't vary greatly in volume this shouldn't be a problem.
Option 4 is the same as option 2, but rather than using impulses and FRFR you use an old school guitar cabinet with a power amplifier of your choosing (like a Fryette or VHT or whatever) This way you don't use impulses but the real thing. You'll probably also freak the soundguy out less with this than the 1800Watt powered speaker. You are limited to one cab sound, but if you like the cab who cares?
Option 5 is probably the most complicated. You use no impulses on the channel going to the power amp which goes on stage just to give you stage volume. You then use impulses on the channel going to FOH... this is Chris Broderick's setup.
On a side note, 1800Watts is ridiculous. Most powerpoints will only let you draw 2400 Watts....