The Mac should be able to connect to any wireless router. The DLink should work fine. You do not need the Airport Extreme.
The Airport Extreme is basically a Mac branded wireless router.
Since it is newer than your DLink, it is possible that it may support a faster protocol. For instance the new Airports will support both Wireless G and Wireless N simutaneously. Depending on how old your DLink is, it might be the older Wireless B, or the newer WIreless G. Unless you bought it in the last couple of years, it is not likely the fastest wireless N.