Use the strat from the "Veteran Tamer" guide on WarcraftPets forum. (Copy pasted for quick viewing)
"Thundering Pandaren SpiritOne thing that wasn't mentioned is that the timing of when you swap in the Grasslands Cottontail after switching in the Carry pet is key to success.
1: Grasslands Cottontail  (S/S) (1,2,1)
2: Sunreaver Micro-Sentry [-] (1,2,2)
3: Carry pet
vs Pandaren Earth Spirit
- Scratch > Burrow
- Continue with Scratch, and use Burrow each time it is off cooldown
- Switch to Sunreaver Micro-Sentry
- Supercharge > Haywire
- Laser > Supercharge > Laser until your Sunreaver Micro-Sentry dies
- Switch to Carry pet > switch to Grasslands Cottontail
- Scratch every turn, unless Darnak has BOTH Stone Rush and Burrow off cooldown (then cast Scratch > Dodge), or he ONLY has Stone Rush off cooldown (then cast Burrow). If you do it right, your Grasslands Cottontail will not sustain any damage from Darnak.
- Notes: Any variant of Rabbit with a speed above 301 will do. The Grasslands Cottontail  just has the best stat distribution for this fight. Flurry is a multi-strike ability, which don't work well against a Shield. As a 1-strike ability, Scratch is better here."
If you switch in the rabbit as one of Darnak's damage abilities comes off of cooldown, your rabbit will instantly die on the swap. In order to avoid this, watch Darnak's cooldowns (using an addon such as PetBattleInfo), and only switch in your rabbit once both Burrow and Stone Rush are on cooldown. This means your Carry pet will probably take some damage, so be prepared to use a pet that can take one or two hits.
Since Burrow has the longest cooldown between Darnak's two damage abilities, watch for Stone Rush and switch your rabbit in right after Stone Rush is used (and only if Burrow is not about to come off of cooldown).
Once your rabbit has successfully lived past the initial swap in, using the above strat against Darnak works like a charm. The cottontail's avoidance abilities are vital and the order should not be ignored.
All of this may seem obvious, but not having done this daily in months and months, I completely forgot the strat and what made it successful. With all of this fresh in my mind and now written down for future reference, hopefully the next battle against the Thundering Pandaren Spirit will go smoothly! :)