Jake, mic the amp for 2 reasons;
1) An extension cabinet will change the sound, maybe considerably, of the deluxe. Part of the sound and charm of this amp is it's open back design and the speaker Fender has matched up to it.
2)Extension cabinets can be pricey, and the right speaker(to your ear) can really run the bill up. Also, unlike guitar amps in general, speaker cabs usually are an item you end up being married to. By this I mean that they are hard to get your money back out of unless you got it really cheap. You would probably rather have the deluxe on its own than sitting on a cab with a different sound and not accomplishing the task you hoped it would.
I would just like to add that if it was really a complimentary option to throw the Deluxe on a cab, there would be a large aftermarket for them, starting with Fender. The Deluxe is one of the most used small club amps ever made, and I would bet nearly every owner has, or would have, been interested in at least trying an extension cab that would give you more volume, but not change the sound. I know the one I had sounded great, and tried plugging it in to a few different cabs, and didn't like the results.
Of course, you may plug your deluxe in to a cab, and find the sound you want. The only rights and wrongs here are the impedance issues regarding loading the output transformers of the amp. NEVER plug your tube amp in to a cabinet that you don't know the impedance of, and NEVER even turn on your tube amp without having a speaker, or other proper loading or testing device, plugged in to it.
Jake, I really think that a Twin is what you want/need. You will never, ever, not be able to hear your amp

. The Twin also sounds good sitting on a 4x12, and its all tube signal path gives you all the goodies perfect for classic Who/Petty/Beatles, and just about everything else. Not to mention that you will be getting the most famous, and arguably the best reverb ever to come on an amp. Keep the Deluxe for recording and rehearsal, but get a twin and never have to worry about tone and volume again.
Just my take on your situation.
