When I see young dogs that are suddenly vomiting but acting relatively normally otherwise, the first couple of things I consider are infectious diseases (think stomach flu), dietary issues (I ate something that didn't agree with me) or foreign body obstructions (I ate something that's blocking my GI tract). These can range from mild things that they get over on their own, up to surgical emergencies.
As long as their breathing is not labored, there is no abdominal distention, and their gums are pink and moist, I usually recommend holding off on giving any food or water for at least 6-8 hours. If they are continuing to vomit though this time, it's time to see the vet. If they stop vomiting, then I start by offering a small portion of water. If they keep that down for more than 2 hours, I offer another small amount of water and a small taste of food (1-2tsp). As long as they continue to tolerate small meals, you can gradually increase the amount of food at each sitting and increase the time in between meals. If they aren't eating at all for >24 hours, this also merits a trip to the vet.
A dose of pepcid (famoitidne) 0.25mg per pound of weight can also help settle tummy troubles, especially if they are related to steroid (like prednisone) administration. Pred can sometime cause stomach ulcers that can lead to nausea and vomiting. It also sounds like Darby may be experiencing one of the other common side effects of steroids - which is excess hunger. Some dogs will eat anything in sight, including inanimate objects like sticks and leaves, when they are on prednisone. It's a very powerful drug and can have amazingly great effect on conditions like allergies, but sometimes the side effects are worse than the thing you were treating in the first place!
With the amount of vomiting you're describing here in the past few hours, it's certainly not a bad idea to get him examined by a vet - it would put my mind at ease to know that he's not got something more severe going on than just a regular GI upset (it'd put yours at ease too I'm sure).
Please let me know what other questions I can answer for you:)