Some D-Link models support updating selected dynamic dns services. The support is however limited and it seems to be that for example you can’t configure it to push updates to ZoneEdit.
A simple workaround is to use the D-Link provided free dynamic dns service, https://www.dlinkddns.com for the dynamic part and the ZoneEdit for static stuff. Simply register a dynamic name at D-Link, configure it to your router and then create a cname record on ZoneEdit on that points to your <something>.dlinkddns.com address.
