Wife living out of USA

Wife left and moved back to southeast Asia. We have no kids or marital assets. I am planning to file the Do it Yourself Divorce papers after one year and one day. My question are as follows: We didn’t have a signed separation agreement, but I know the exact day. Is there a problem not having a signed agreement? When sending her the papers, she’ll be required to sign and notarize them. As far as I know they don’t have Notary Publics in her country, then what? What if, she doesn’t sign them?

If your wife will not file anything contesting the actual date of separation your allegation in the Complaint for divorce will be sufficient proof of the date of separation.
She need not sign or notarize anything, you will just need proof that she was served with the Complaint (certified mail receipt).