When I first got into pet-battles/collecting I also wanted to upgrade the Proto-Drake Whelp. But you can catch a rare Emerald Proto-Drake Whelp, have a better rare quality drake (better for pet-battles), and still have that look. Only difference is that the emerald is green. But he's a mean green!
You might want to check out this list in making your choice:viewtopic.php?f=2&t=2978
Personally, this early into pet collecting, I would recommend you hang onto that stone until you get to know all the pets better. What you use a stone on will depend entirely on you. But you may ask yourself first what you intend to do in the future.
a) Will I get into pet PVP?
b) Would I like to get into the Timeless Tournament to get the Celestial Pets?
c) I don't care about either of those, and just want to collect wild pets.
If you chose either a or b, you might want to use that stone wisely, as some pets are far better at battles than others.
From the list above, here are some of the better battle-pets that need a stone to make rare.
Azure Crane Chick (P/P or S/S)
Cornish Rex Cat (P/P)
Curious Wolver Pup
Death Adder Hatchling (P/P or S/S)
Gilnean Raven (S/S)
Mechanical Pandaren Dragonling
Red Dragonhawk Hatchling (P/S)
Scooter the Snail (though you can catch "Shimmershell Snail" in the same breed)
Silver Dragonhawk Hatchling (S/S)
Yellow Moth (P/P)
Those are the best battle-worthy Uncommon only pets (forgive me if I left any out
. . .And then there are wild pets that you may find it very difficult to obtain depending on your server. On high-pop servers you will
have a hard time getting a Minfernal or a Jade Oozeling in any breed, let alone a good breed.
But in the end, as you battle you will be sure to pick up more stones. The stones that aren't marked for a particular pet family... well, most of us wouldn't use one on just anything, as the poster above me pointed out.