After reading through an unofficial help thread for newbies, I saw it listed only 3 options for reviving knocked out pets: Revival Draught, Healer, or simply wait it out.

There's a faster way to reviving pets than simply waiting for their health to recover and it's considerably cheaper than using a healer, but it takes a bit more work.

Step 1: Remove fainted pets from Party: You can go to Explore > Party, and then click the red minus to remove the fainted pets from your party

Step 2: Revive via Stables: Go to Account > Stables and at the top of the screen there should be a button that says "Revive Pets" click on it and you have the option to revive all pets in a stable or across all stables, but it only costs 100 gold per pet to revive them to full health.

Step 3: Add the pets back to your party: Head back to Explore > Party and towards the bottom use the Select Pet box to pull up the pet(s) to add back to the party and add them by clicking on the green + in the upper-right corner of the pet's info box.