Wouldn't be a dragon pet a bit unbalancing? Unless it happens in process of that egg laying monster turning on your party along with its pet dragon, in that case it is OK.
This could be a baby / young dragon, which she must raise so that in the epilogue we will be shown how she rides on it. Or it could be an adult dragon at a stage in the game when it doesn't break her.
In the game, the maximum level is 12-13 (maybe even higher), and that flying dragon in the git patrol has level 4. If Laezel has his own dragon at level 10, it will not be imbalanced