And it just hangs on waiting for the "receiving DS"? Do your stock apps work fine i.e friends list, streetpass etc? As long as you can connect online with the 3DS I wouldn't assume it was your network. If I were you and not getting any error codes or anything, I would power cycle my 3ds and my router, remove the battery, remove the SD card and try again. All you can really do is troubleshoot each potential "error" to determine the cause short of finding a specific problem/solution.
That and I hope you didn't miss the part where you have to choose the receiving 3DS on your source 3DS after initiating the transfer.....Else the target DS will just stay "connecting".
Source System
1.From the HOME Menu tap the System Settings Icon and then "Open."
2.Tap "Other Settings."
3.Tap "3" and then "System Transfer."
4.Tap "Transfer from Nintendo 3DS."
5.Read the information about the transfer and tap "Agree"
6.The number of transfers will display. Tap "Yes" to initiate the transfer.
7.Tap "Send from This System."
Target System
8.From the HOME Menu tap the System Settings Icon and then "Open."
9.Tap "Other Settings."
10.Tap "3" and then "System Transfer."
11.Tap "Transfer from Nintendo 3DS.
12.Read the information about the transfer and tap "Agree"
13.The number of transfers will display. Tap "Yes" to initiate the transfer.
14.Tap "Receive from Nintendo 3DS."
Source System
15.Select the system that will receive the transfer.
Target System
16.Tap "Yes" to accept the transfer.