Unfortunately, but it is kinda hard to know for sure, but my guess is the same as yours that there might be a problem with either your 3DS and/or copy of Animal Crossing, sorry.
But even if it isn't and might be some type of Internet or wireless router setting problem, probably the best thing to do is give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, and one of the service representatives can do some over the phone troubleshooting to determine exactly what might be causing this, and then talk you through any needed steps to correct it.
And if nothing corrects it on your end, then they can set up the repair process for you at the same time.