If you dont owe anything, you dont really need an extension.

Your spouse passes the substantial presence test for 2016, but she is a dual status alien. Dual status aliens cannot file a joint return. If she had no income after she came to the US, she would not have to file a return at all, otherwise a dual status return. You would file as married filing separately in this case.

You would have the option to treat her as resident alien for the entire year by adding a statement to the return making this election, but she would have to report worldwide income for the entire year on the joint return.

Anyway, you should wait to file your return until she receives her SSN.