i would start doing that soon as in like maybe today or 2morrow. because even when you do the address change, you will still recive mail at your current address and not all mail will be fowarded to the new address. just to be safe u get all your mail, thats what i would do. and by the time you move, you should be recieving all your mail. hope this helps.
If you use this link, you can change your address now but pick the day you actually want your mail to start getting forwarded. You can pick the exact day you move in if you'd like. It's through the USPS so the switch actually happens when you want it to.
I used it a couple months ago when I moved and as soon as my address was confirmed (about a day) my mail began getting forwarded.