Yogi Bear, perhaps, for Yellowstone (Jellystone) National Park?
When I was 18 years old, I took a Greyhound Bus from Pittsburgh, PA to Sacramento, CA. I remember a short layover in Cheyenne, Wyoming during Cheyenne Days. It was 3 am though, so I walked around for ten minutes then reboarded. At 3 am, Cheyenne was really quiet.
ETA: BTW, this was in 1976. Greyhound had a $76 promotion. For $76 you could travel for up to a month in one direction. I spent about a week going west.
You could wear a cube and have like a topography of the things that Wyoming is famous for, and spread them out sparsly over the surface of the cube.
Yeah, my mind works that way. 
Yep, it’s called Frontier Days. It’s the largest outdoor rodeo festival in the world, and has been held annually since 1897 - hence the nickname “Grandaddy of 'Em All.” Not surprisingly this is the only time of the year that anything remotely exciting happens in Cheyenne.
Nuclear missile silos. A Trident nuke or similar should be pretty easy to make. And I’ll bet she’ll be unique!
tim
If you’re feeling especially lazy, you can always go the Homer Simpson or Ralph Wiggum’s parents route.
Just put together an outfit of clothing and accessories purchased from the J.C. Penney Company. Subtle yet appropriate.
I associate Wyoming with Tim Sandlin novels, but I don’t think many people would get it if you had her dress like a bride and carry a football, a la Sex and Sunsets.
Wyoming native and current resident here.
I, for one, am in favor of the Sufferagette outfit. It is unexpected, historical, educational, and echoes the values of the Girl Scout Program (as I understand them). It might give you an opportunity to teach her a little about the early history of the civil rights movement, too.
On the other end of the spectrum, she could go as “Cattle Kate”, who was wrongfully lynched for rustling about 100 years ago. (Cowgirl outfit with a noose - what, too morbid or inappropriate).
Also, instead of a cowgirl, how about a mountainman/furtrapper. Also very historical.
There is still a lot of native populations here. If she could do it with sensitivity, maybe something to celebrate the Shoshoni Indians.
Maybe a park ranger? A close encounter alien? A uranium miner?
If there is anything I can do to help, feel free to message me.
I always think of a big orange square. Probably that was its color on my elementary school map.
I’ve done this, with a twist.
My halloween costume was a cardboard box. The official Wyoming map (at least in 1982) had the state’s topography drawn onto it. Why not - it’s so sparse, there aren’t a lot of roads to clutter it up. So I cut the key off the map, so that what remained looked a lot like, well, Wyoming. I put clear Contact paper over the map to mount it onto the front of the cardboard box.
Then (heh heh) I found Old Faithful on the map, put a hole through it, and had a water-filled plant sprayer that I shot up the room with about every hour or so. I even had a cheap alarm clock in the box to tell me when the time was up. After a while (thanks, Pavlov) the sound of the clock could clear the room…
In answer to the OP, I think of freedom. It’s the least regulated place I’ve ever lived in. There weren’t a lot of laws to protect you from yourself, which was fine with me.
I also think of wind, cold, wide open spaces, and people who REALLY drink.
I only lived there for three years, but loved it.
Wyoming Knott from The Moon is a Harsh Mistress. Try a pressure suit. 
Or “afro” makeup and a tight red dress…
I think of Old Faithful. You could dress her in shades of taupe and brown, and make a hat with a big “geyser” of tinsel sticking up from it.
Love Kilvert’s Pagan’s idea, though.
Reloy3’s suffragette suggestion is a good one, too. I just wonder if it will be a little too esoteric for the spectators to “get.”
Would you mind answering a couple of questions for me?
How on earth did she end up with Wyoming of all places? Were all 50 states assigned? I have no beef (ha!) with Wyoming at all, and I’d love to visit someday, but it really is a stinker of a state to have to make a costume out of.
And would you please let us know what other “state’s” costumes are? Especially New Jersey!
My first thought too.
There’s a girl in
Wyoming
And they’re combing
Wyoming
To find the man in white
Who was out with her that night…
Yeah, I know, that’s even less than less than helpful.
“The Equality State” - how about a suffragette? It’s not easily identifiable, but back in my Girl Scout days at least it would have gotten points among the leaders for creativity and women’s liberation sentiments
Since Wyoming is the least populous state, she should just not show up at all to symbolize the desolation. There. Saved you a couple hours of boredom. 
Wyoming has had several women’s suffrage ‘firsts’. First woman to vote, first female juror, first female governor, first female Justice of the Peace and so on.
I sometimes wonder if the women’s suffrage leadership might have been an effort to get more women into the state. There’s always been a shortage of them.
Wyoming has a dirt airstrip officially named the Greater Green River Intergalactic Spaceport.
Major snaps for that one.
What do I associate with Wyoming?
Mustangs and the BLM. IIRC, they have regular round-ups and sales in that state.