Could you learn and give her one shot? It's no fun, I'll admit, but you could give her an extra treat to make up for it (dessert was always a must at our house).
We have taken biologics with us to many countries - England, India, Germany and recently, Mexico. It's a bit of a pain, but not too bad. We take them on board with ice and they stay cold -- even on a 14 hour flight to India! We get a doctor's note so TSA does not bother us and they never have.
I don't know about your kiddo, but if we are even one day late, both my girls really feel it.
Both my girls have had to miss shots in the past for infections/wisdom teeth surgery and both really flared. My older daughter just missed two Humira shots before she flared and that flare eventually led to a med change. That's obviously one of the worst case scenarios, but it was no fun.
Those experiences have made me VERY wary of skipping even one shot.