I am not JoeSchmuck and I don't know if he can tell whether his lights blink faster than yours or not. :-)
(Just kidding.)
But - and I reserve the right to be wrong - I think kiddie scripts basically work by running a port scan and then trying to login using every known login method (ftp, telnet, ssh, whatever) on every open port they find. Not very sophisticated, but computer time is cheap. So they will get to you no matter what port you use. And there are zillions of users using simple passwords that are there on every password list, so they will get access somewhere sooner of later. Maybe not at your box.
Using a different port might make a difference for people when their ISP does not allow access to some standard ports. Otherwise I would not count for security on the obscurity of some high port.
As far as what can they do once they are in... I don't know. But your DNS-321 is running a firmware and unlike your Linux/Windows/OSX desktop it does not get regular security patches. So if there is a security hole in the FTP server program and it is found this week, your box will run the current, unsecure version a year from now still, most likely. (Dlink does not have the resources to maintain regular patches, sorry.) And if they can get to a shell prompt they can sniff your internal network, etc.
I don't want to be an alarmist and I think if you use complex passwords you are probably better than most, but I would not bet my money on the security of any FTP server.
One solution is (maybe a bit more complex and involved) is to use two routers. Behind the first router you setup your 'dirty/public' machines, where you have open ports. (You FTP server, web server, whatever.) And then you keep you 'safe' machines behind another router on a separate network and allow no outside access to that. I know, it is a bit paranoid, but better than wishful thinking and considering the price of a router these days, it is not that expensive. The real problem is that you will need two of everything - including two servers.
You have to separate your data to 'internal/secure' and 'external/dirty'. Photos you publish for your family you put on the outside server. Your financial files go to your internal server. Again, considering the price of a DNS-321, it is not that expensive. But soon you start thinking if you really need to setup / maintain a whole public server, or if you were better off to use some public hosting option, that can be had for $5 a month.
I am no security expert, I just don't want you to have the fake feeling of security just because you move your FTP connection to a high port.