She's a fully grown dragon, who is loyal only to her rider,
Gira_.
She saw Gira, and Gira instantly took a loving to the girl, taking her in a her own daughter. Before the girl had hatched, Gira had found the egg abandoned on a mountain, and had guarded it with love until it hatched. Gira named Gemma because her egg was hidden in the stones, like a little gem. That is why, when Gemma hatched, the sword girl was the first thing she saw.