Upvote:5
Your passport just needs to be valid for at least 6 months at the time you plan to enter the US. They will issue you a visa as long as your planned date of entry is at least 6 months before the expiration date of your passport.
The rule about needing to have a passport valid for at least 6 months beyond the period of stay basically means that the immigration officer at entry will not put on your I-94 an admit-until date that is later than 6 months before your passport expires. However, J1 are usually admitted for "D/S" on their I-94, not a date. So that rule doesn't apply to you, other than needing to have a passport valid for at least 6 months when you enter.