Yes, all Airstreams should have rear bumpers IMO.
Is that a solar panel you also added? What is the combined weight of everything you have added to the rear? The new weight back there could add to sway issues IMO, especially if your fresh water tank is also located aft of the [single?] axle like our FC20. Plenty of threads about sway, like the "Out of Control Sway" one.
Caution advised, including some test runs with you trying to induce sway, while having one hand ready on the brake controller, in order to dampen any trailer sway ASAP. Important that you weigh your rig carefully, with any weight distribution hooked up. Also get an exact reading for your tongue weight, as the new rear weights will certainly affect that. Reducing the tongue weight promotes sway.