Congrats on your first trailer!
You definitely will need a sway bar, so get one right away. As far as hitch-weight goes... yes, you have a relatively light hitch weight. But your trailer also has two side-storage compartments up front and more storage under the queen bed. Most people utilize these spaces and it will add a significant amount of pounds to your hitch weight, so I wouldn't worry too much if you use these spaces. Just don't over-do it and you'll be fine.