Writing a driver for a wireless usb dongle for an AVR microcontroller
You will have to get a USB sniffer to be able to sniff the protocol. Otherwise, even if you have a USB stack, you won't know what kind of data to send and receive. Moreover, the driver required to run the USB dongle is likely to be very large, perhaps too large to fit in the AVR micro's flash. I recommend that you pick up a ready made module such as TI's CC3000 or another one.

For USB a good reference is USB Complete

[Edit]: I really recommend you look at TI's CC3000 module. It's throughput can reach 4Mbps, and this is what you should expect from a microcontroller based solution.