Actually, this is totally doable. Attack order in Pokemon games is all based on which Pokemon has a higher speed stat, and I think it's safe to say Articuno is fast than "Bunnymon"(which for the record sounds more like a Digimon than a Pokemon)

In addition to what's mentioned above, there's what's known as priority attacks, which always go first. In either of these cases, though, Bunnymon would be guaranteed the next attack. There's no "preemptive strike" like in a lot of RPGs. I suppose in theory, Articuno could have some sort of terrible priority move that causes flinch (prevents the opponent from moving that turn) but that seems unbalanced even by the standards of today's Pokemon games, which gave us a Pokemon that's literally had to be banned from the tier designed for Pokemon that are too damn powerful for normal play.