A Song Of Ice And Fire

My question: does that indicate that weirwood is impervious to dragon fire?

I'm unsure. My theory is that Ryan Condal (and GRRM by extension) are hinting at the magical properties of weirwood and, more specifically, that it could harm dragons.

During Aegon's Conquest, Brandon Snow (Torrhen Stark's bastard brother) offered to cross the Trident alone at night, sneak into the Targaryen camp, and assassinate the dragons while they slept. So, at the very least, Brandon thought he had something powerful enough (and maybe fireproof—or at least resistant) to get the job done.

The connection to Weirwood might be in ADwD. In that book, one of the visions Bran has through the Winterfell heart tree is of "a pale, fierce, and dark-eyed young man" slicing three branches off the weirwood and shaping them into arrows. I've read before that this may be Brandon Snow, preparing Weirwood arrows to kill the three Targaryen dragons.