Thaumaturge
Wandering. Not lost. (He/they)
Does it matter? The half-dragon will be dead in 3 rounds...
Funny. I actually had to reread that. I originally read that as "Does it matter? The dragonborn will be dead in 3 rounds..." Because of...plot...stuff. I even launched into a defense of why it would matter even though the PC would go down quickly.

At least once in the adventure, the PC is unlikely to smack the half-dragon quite so handedly.
PC Dragonborn: "These are the ears of the last half-dragon that called me runt. Guess I get to add yours to my necklace."
Yeah. That's an unlikely outcome for the event I have in mind. Possible, I suppose, but unlikely. And if it happens on the second (or third) such encounter, then it'll show pretty cool growth in power.
I'm thinking that Wyrmling would be a good one though. Or Gecko.
My only hesitation on "wyrmling" is that it's actually a step up for both the half-dragon and the dragonborn. I mean, a wyrmling is at least a dragon.
Writing that makes me think "pseudodragon" might work better.
Thaumaturge.