To apply for a J-1 visa, your girlfriend will either have to find an employer who is a "designated exchange visitor program sponsor" and can provide her with the form she needs to send in with her visa application - or she needs to sign up with an approved exchange work program.

It is usually not possible to change from a tourist visa to a work visa while remaining in the US. At a minimum they normally require you to go back home to file the application (which takes at least a few months). Requesting a change is more or less an admission that you entered the country under false pretenses (i.e. to look for work rather than as a "real" tourist).
Cheers,
Bev