Have you asked her out yet?
You've already been pre-vetted with the cousin matchmaker connection, and you'll have plenty of time to get to know each other in person when you meet up.
She saw your
message. She might be busy, but I'd go ahead and suggest a specific date and time and activity - even if you are double texting. There is still time for this weekend (next weekend is fine too): small hike in a popular park, mini-golf, etc if you need some quick ideas. Something that should take about 2 hours. With maybe some ice cream or similar afterwards (no need to mention this, but plan it out).
She might be interpreting your 30 minute delay as a game technique. Girls know about the 3-day rule and waiting to reply and that sort of thing.
The ball is in YOUR court. In her mind, she's already expressed quite a bit of interest. I would have already asked her out in my first or second text in this situation. You still have time, plan something out and send her a message.