This strategy is especially hard (read nigh impossible) to beat. The three units are actually the key why it is so powerful, but actually you start with roaches for T1 dominance, then add quens. Queen + Roach alone pretty much dominates anything protoss, and fares very well vs Marine+Marauder as well.
On T2 Terran will just die due to fungals (Infestor should be the first unit you get on T2 versus T). Protoss will actually get ahead due to Archons and Immortals. If facing a toss, Hydras are next, and then a few Infestors.
At T3 you will pull your ace in the hole, the Broodlord. It has a perfect synergy with slowzerg (read: no speed upgrades, no creep) units such as Queen and Infestor. Queens provide AA for the BLs, while Infestor stops everything out of range of BLs. Protoss is pretty much screwed at this point, as he can not fight the Broodlords due to your army + fungals blocking, and broodlings constantly spawning (toss units are weak vs anything light).
There's two units that can break this: Vikings and Corruptors. Vikings are really crappy and you should not be afraid of them. Fungal + Queens kill them in no time, and Queens heal your Broodlords if they get damaged. Corruptors are only available to zerg, and to counter them, get more Infestors, and chain-fungal them to death (queens will help with damage).
If any air unit number would get out of hand, well, you have the best AA unit of the game: Corruptor. They are extra powerful with Queen support.
Now this strategy has gotten to the point, where I feel guilty (and kind of bored) when random rolls me zerg. This is so easy and powerful across all stages of the game. It pretty much only fails if your allies are so bad that you never control the middle, and you get overwhelmed.