I think any Mini PCIe wifi card should work in any computer which has a true Mini PCIe slot available. Whether it's a laptop or netbook or desktop, whether it has an AMD CPU or Intel, Atom or Core 2 or whatever.
Just a couple concerns...
Not all "Mini PCIe" slots are actually full Mini PCIe slots, but Wifi slots usually are. SSD
and WWAN slots in Dell Minis are not.
Mini PCIe Wifi cards are available in full and half height versions. Older computers, like the 9 use the full height. Newer ones use half. But the slots are the same, a wrong height card will work in the slot, it just might not fit physically in the computer and the screw holes won't line up. (really old laptops use Mini PCI cards, which are completely incompatible)
Also, I think some laptops don't use Mini PCIe cards for WiFI.
Another BIG concern is companies which cripple their Wifi slots to only run "approved" cards. A normal Wifi card won't work. I think HP/Compaq is notorious for this. But I've had no problem swapping Wifi cards around my Dells.
Good luck with yours.