Here is a good FAQ with some basic questions answered for J1 Visas:
This Google Answers Thread is very similar to your question:
Quote from hummer-ga
1) Get married (congrats! 8-) - Yes, while you still hold your J-1 status.
2) Soon after the wedding, your husband will file a Petition for Alien
Relative, Form I-130 and I believe you can file your Adjustment of
Status, Form I-485 at the same time, but you will need to check with
your local USCIS office for any special local instructions first.
FORM I-130, Petition for Alien Relative
The I-485 - Application to Register Permanent Residence or Adjust Status
If you are the immediate relative (spouse, parent or unmarried child
under 21 years old) of a U.S. citizen, submit the following forms:
* I-485, Application to Register Permanent Residence or to Adjust Status
* G-325A, Biographic Information
* Either your original I-130, Petition for Alien Relative (if you
are filing concurrently)
* I-864, Affidavit of Support
* I-693, Medical Examination of Aliens Seeking Adjustment of Status
* All required supporting documentation as listed on the above forms.
You may download a package of all of these forms in PDF format.
"The I-485 in this case may be filed at the same time as the visa
petition (I-130) which is filed by the U.S. citizen or lawful
permanent resident. See your local office "About Us" page for any
special local instructions including any local forms needed to apply
for permanent residence."
Petition for Alien Relative
"NOTE: If the I-130 petition is being filed concurrently with Form
I-485, Application to Register Permanent Residence or to Adjust
Status, submit both forms at the local INS office having jurisdiction
over the place where the I-485 applicant
resides. Applicants who reside in the jurisdiction of the Baltimore,
MD, District Office should submit the I-130 petition
and the Form I-485 concurrently to the USINS Vermont Service Center,
75 Lower Welden Street, St. Albans, VT 05479-0001.
If you live in Alabama, Arkansas, Florida, Georgia, Kentucky,
Louisiana, Mississippi, New Mexico, North Carolina,
Oklahoma, South Carolina, Tennessee or Texas, mail this petition to:
USINS Texas Service Center, P.O. Box 850919, Mesquite,TX 75185-0919.
If you live in Arizona, California, Guam, Hawaii or Nevada, mail this
petition to: USINS California Service Center, P.O. Box 10130, Laguna
Niguel, CA 92607-0130.
If you live in Alaska, Colorado, Idaho, Illinois, Indiana, Iowa,
Kansas, Michigan, Minnesota, Missouri, Montana, Nebraska, North
Dakota, Ohio, Oregon, South Dakota, Utah, Washington, Wisconsin or
Wyoming, mail this petition to: USINS Nebraska Service Center, P.O.
Box 87130, Lincoln, NE 68501-7130.
Hummer suggested finishing out the program. I looked through the
documentation for the J visas and found this:
Sponsors shall notify the Department
of State in writing when:
(1) The exchange visitor has withdrawn
from or completed a program
thirty (30) or more days prior to the
ending date on his or her Form DS?
(2) The exchange visitor has been terminated
from his or her program.
She cannot just leave the program and not tell anyone, but if her host
family contacts the State Department and lets them know that she has
completed the program early you won't have to wait 'til the entire
program is up.
1. Get Married
2. Submit concurrent filing of I-130 and I-485 in CA (mailed to where
you would submit the I-485)
3. Submit I-765, Application for Employment Authorization
4. Don't leave Au Pair program until hosts have contacted the State
Department and you paperwork is far enough along to be legal.
Please get in touch with all concerned authorities before doing
anything - there are so many little details that could effect how you
should proceed, it is impossible for me to tell you exactly what to do
in this public venue. You need to contact your local immigration
office, read your au pair contract, and contact an experienced
immigration lawyer for advice.
I hope this has given you some direction.
Please request clarification if you require more information.