Since this apparently hasn't been followed up on and I recently finished reading
Harry is a Dragon and that's OK myself, I'll add my recommendation. Non-spoilery synopsis:
It's mostly slice of life and comedy, building on the premise that for mysterious reasons Harry Potter turns into a small dragon when he's about 5, with an anti-Muggle effect ensuring that nobody but him notices until Hagrid shows up. Most everything else that changes comes from that, eventually sending canon well off the rails. It's an interesting variation on the common idea of giving a canon character a power up since rather than making him super-
powerful, he's more nigh-indestructible. Also absurdly omnivorous.
As for Dumbledore, this version is benevolent, combining amusing eccentricity with cleverness masked by that eccentricity.
As any rate, due to Harry's presence as a dragon and his actions many events go differently and characters develop in different directions. One moderately spoilery example:
His presence as a dragon is leveraged by Dumbledore to allow the introduction of nonhuman students.