From my experience and 3 moves later (all in the same phone number prefix area) I simply had my line transferred. So if you are moving within the same area I suggest trying to have it all transferred, but go to your local Telkom shop to get it sorted, try avoiding the call centre if possible.
With each move the transfer was done successfully, although I had to drop tools and run each time to give the techies access to my premises. The last time they did it on the morning of 24 December, goes to show what can be done. If I was you, try the transfer thing first.