Like Allison said, there no reason Bliss can't event, especially since you aren't planning on going past Novice. Take the winter and get her conditioned and hone in on your dressage skills. Eventing is won and lost in the dressage arena. Plus the better your dressage, the better your jumping.
I do a lot of unrecognized events and like Wren said.... you'll see all sorts. I've seen a full Clydesdale doing Novice and something just shy of being a mini packing the cutest kid around xc. Draft crosses are very popular at the lower levels.
If your horse says no, you either asked the wrong question or asked the question wrong
And God took a handful of southerly wind, blew His breath over it and created the horse