You are taking a huge chance if you ask me. Who knows what the consequences are if you get caught. Could they take her from you if you got caught? What if your flight is delayed and you sit on the runway in a hot airplane and your suggie is in a pouch on top of that. Deydration is a concern and if you do give her water, you have to be soooo careful she doesn't freak and get away from you.
Self medicating her isn't a choice as the littlest mistake could have fatal results since they weigh so little. A vet could tell you what your options are.
My Mom was trying to talk me into flying to visit and I told her that I couldn't take the suggies with me on the plane and she said who would know. I explained that they make this god awful noise that sounds kind of like a grinder and that it would be a sure giveaway. My Mom said just move your lips like it is you making the noise

I just chuckle when I think about that.
I am picky about someone else taking care of them also but perhaps an exotic vet in your area could recommend a pet sitter who wouldn't mind having them for a month? Good luck with your travel.