Amazon sells basic generic backpacking packs for under $40. They aren't the best by a long shot, but they will get you there.
I'm a fan of buying good quality things that will work for a long time, but at the same time, a mediocre pack for $40 that will easily handle a mile hike in to a site might be good to have on hand. It will at least teach you enough about what you like and don't like. You'll learn what to look for in a real pack.
You have rope. You can lash the tent and pad to the top of the pack if they don't fit inside. Or carry one under each arm. A mile is only half an hour. You can do that.
I checked out the park at the link you provided and looked at it in Google Earth. The trail to the camping area is pretty much all wooded with a little bit of up and down, but not much. Looks like a nice place, and the trail that goes to the bluffs looks really cool. After dropping your stuff off at the site, you should check that out.