The possibility of full time employment is much lower than part time. Sexual assaults are rarely prescheduled, so the majority of the actual cases are performed as "on-call" responses. Follow-ups, or "chronic clinics" in the pediatric realm are prescheduled.
Some of us are employed by ED's, some by advocacy centers, and some-like myself- are independent contractors, paid an on-call pay and fee for service via grant funding.
SANE nursing is a wonderful, fulfilling specialty. One where you will never get rich, or be guaranteed a full night sleep when on call.
If you really want to commit to this specialty see where your local resources are. Where are exams done in your area? ED's, community advocacy centers, there are expanding options. If you can't find your resources call your local law enforcement, sex crimes division. They definately know what system is used.
Good luck, and just shoot back if you have any more questions, Amy