Any step stool you make or get could have problems with uneven ground but those step stools with legs will be less stable so, yes, if you make yours, you'll want to make individually adjustable legs. The Vardo one (the two legged ladder style) that you drew might be the easiest to make and also the easiest to create adjustable legs for. You would need a way to attach the top to the trailer's deck, though. Once you did that, it would most likely be reasonably stable. Maybe some bunk bed hooks? In my opinion, however, ladder steps of any kind make it harder to carry loads into the trailer cabin and tend to be slippery in wet conditions.
I have had next to no problems with my purchased one because it has a solid base (but I understand your desire to make your Vardo look its best). The roughly 16" height has worked very well, whether the trailer was jacked up to 18" or sitting at 15". It also works well and is not damaged by rainy weather and soggy-boggy soil. Being a painter, you might be able to incorporate it by painting the sides of it with a Vardo-like design and make it a feature!
You showed us a picture of what looked like a handmade step stool, so I thought you'd already decided. Were those somebody else's work or used for another purpose?