It might be weird, in the sense that it's not "normal" relationship progression. But really, there's no set rules or path needed to take. My situation is weird, I've traveled 8 times (mostly to across the country) in 6 months to be with someone I'm not even dating. It's working now, and I'm having fun and enjoying it. That's all that it comes down to. So yeah, it weird, as an outsider but there's nothing wrong with it.
So have fun Alli, and enjoy it! But maybe not mention your ex in here anymore.