ACGirl--
I know that when D Phi E places Chapter Advisors, we try to get women that are graduated for at least a year or two. But there are certainly roles you can take on the minute you graduate. We have Membership Recruitment Advisors, and they are normally younger women because they are in touch with why women rush and so forth. That is a regional position within our group.
Best of luck...volunteering to work with collegiate chapters has been one of the most worthwhile decisions I've made (I'm a regional advisor now).