It's usually better to have the same vendor, and something that the vendor supports. Mixing stuff means you get to own more of the "fun" of getting things to work. Welcome to that "fun"...
Caveat: I don't have experience with mixing a D-Link DAP-1520 Range Extender with a Netgear N750 wireless router (WNDR4300), and I'd not expect a whole lot of folks around the Apple OS X Mountain Lion forums would either. Maybe try here?
If the range extender unit isn't showing up at all, try a reset (check the docs for how to do that), then — if it's not working after a reset — then it's probably not working right.
For cases with spotty coverage, I've found configuring Wi-Fi devices as Access Points (APs) with wired backhaul is usually easier. With multiple routers, you're going to be learning about avoiding overlapping networks, and subnet routing. (Though I've not tried a range extender here so I don't know if that shows up as an Access Point or as a router — Apple does have WDS with some of their AirPort and Time Capsule devices, for when that wired connection just isn't feasible.)
WPS is wildly insecure way to configure the Wi-Fi settings.