How do you know she didn't have Jasmine in her earlier?
What was her demon if it wasn't Jasmine?
I think she need to go to the higher plane to allow Jasmine to emerge, but already had Jasmine in her.
Why? First Skip who later admitted to working for Jasmine was her spirt guide. He offered her the initial choice as well as taking her to the higher plane. Secondly, and more tellingly the nature of the demonic essence inside Cordy points to a present although unaware Jasmine.
Cordy glowed the same way Jasmine later glowed after becoming part demon. She felt no pain at all from the visions, which means that whatever was in her was very powerful. She was also able to cleanse Connor and drive the water-sucking squid monsters from the hotel. These are not the actions of an ordinary part-demon person. Clearly whatever was in Cordy was frightenly powerful, and since the least complex explanation is that it was Jasmine and not some other force I am inclined to go with Jasmine.
Also, Cordy eventually died after Jasmine was born. When she was knocked out of her body, Skip told her that she would slip into a coma and die when she had the next vision if she stayed human. That is exactly what happened.
If Cordy still had demon essence in her why would she die after having a vision? Remember that Whedon & co. like arching storylines so its quite probable that an earlier episode holds the key to what happened to Cordy.