Hello and welcome to the forums!
Is there a boarding service at the vet where they could keep an eye on her foot? I agree with Randy that it could cause an infection if not treated properly. In the mean time, I would do as Randy suggested and flush it out with warm saline solution and if she looks in pain or the area is swollen, you can put some room-temperature chamomile tea as this is a known anti-inflammatory agent. Aloe vera gel from the plant helps too and it is non-toxic to budgies, so after you clean it with the saline/tea you can put a thin layer on the affected area and it will help the foot heal.
I hope your little girl is okay! I would definitely call your avian vet today at least to let him know what's going on, even if you can't take her today. It would be good to see if you can leave her there while you're gone or something if the cut is really bad, just to prevent an infection.
It's good to have you on the forums! We'd love to meet your little girl sometime so feel free to post pictures of her when you have the chance

We'd love to help with any other questions, too, so please don't hesitate to ask
:welcome: and hope to see you around!