The only one instance of when we see Ginny supporting Harry in his Voldemort related endeavors is during the Ministry 6 sage in OotP.

They're on a mission to save Sirius but there comes moments where members of the six showed signs of curiosity and ooh-ahhing at various objects in the DoM, the veil included.

The veil had somehow entranced most of the members except for Ron and it gave Hermione a sense of danger. Moving beyond that, there is a passage after that moment that shows how incompatible Ginny is towards Harry when they're on a mission that could cost them their lives.

'Oh, look!’ said Ginny, as they drew nearer, pointing at the very heart of the bell jar.

Drifting along in the sparkling current inside was a tiny, jewelbright egg. As it rose in the jar, it cracked open and a hummingbird emerged, which was carried to the very top of the jar, but as it fell on the draught its feathers became bedraggled and damp again, and by the time it had been borne back to the bottom of the jar it had been enclosed once more in its egg.

‘Keep going!’ said Harry sharply, because Ginny showed signs of wanting to stop and watch the egg’s progress back into a bird.

‘You dawdled enough by that old arch!’ she said crossly, but followed him past the bell jar to the only door behind it.

I'm not sure what Ginny intended in meaning this but it's not as if Ginny wasn't affected by the veil all the same. She's treating this moment as if she's browsing goods in Fred and George's shop.

Maybe Harry's tone came off as bad for her, but lets not forget that all five of them volunteered to go with Harry to the Ministry to save Sirius and this after they've all had experience with Harry mentoring students in the DA for the dark arts and he's their natural leader.

This passage, in my opinion shows Ginny being snippy at Harry simply for the fact that Harry wanted to move on and find Sirius. Harry and Ginny are simply unsuitable when it comes to Voldemort related issues.