I was told that in order to do a self move you must:
1. Have orders in hand
2. Clear every aspect of your move with the move office before spending on it.
Any truth to the second part?
The housing office will not deny you a do-it-yourself (DITY) move. I mean, nothing is certain in the military, but in three decades in and around the Army I've never seen it happen.
All you really need are your orders, mainly because the moving office probably won't even field your phone calls until you have them. Depending on what type of DITY move you choose (there are options), they'll probably want to at least estimate the weight of your household goods. I've seen this done over the phone and I've seen them send someone to your home.
From that point, it can happen as quickly as you want it to, especially if you're doing the driving yourself. Of course, there are timing and storage issues to consider, but those are separate matters.
I'm sure there are some great websites out there that detail the process. I suggest researching those sites to find out what option is best for you, how much are you entitled to ship (usually based off of rank and dependents), and what documentation will be required. Save everything, in triplicate.
ETA: Q: Any truth to the second part? A: Not really. If you do a true DITY move, meaning you pack, load, ship, store, unload, and unpack everything yourself, then the details (and the liability) are almost completely up to you.