I'm pretty sure the absolute minimum is about 90 days.
You can definitely plan an Escape wedding in that amount of time, it might be a little harder to do a Wishes event that quickly, but I have no doubt Disney could pull it off if necessary.
The only thing about waiting longer is that you may have to be flexible with your preferences. The venue you want may not be available at the exact time and day you want. If you want that particular venue, you may have to adjust your time or day. If you want a particular day, you may need to adjust your location or time.
We used the basic Escape package (well, it was still called the Intimate back then) and called Disney in April for a September wedding. Originally we got everything we wanted (location, day, time) but about 90 days before the wedding we changed locations. It all worked out just fine!
Congratulations and good luck!