Your bike is fine. "Hybrid" is just a category recently made up to sell more bikes, and it doesn't suggest that you can only use it for . . . what, hybridizing? A picture of your bike reveals that it's a normal modern bike that's perfectly appropriate for touring as long as it is sized and adjusted to fit your body, and geared low enough let you go up hills comfortably.

Also: people tour across the United States with 32-spoke wheels all the time -- if you're not some combination of overweight, carrying way too much stuff, and/or touring across boulder fields, then you'll be fine. These wheels are probably way stronger than most of the ones people used touring thirty years ago.

You sound way more interested in having fun touring than constructing the Platonic ideal of touring bike. If that's accurate, you're probably all set to go already!