If your wife is a nonresident alien (she hasn't met the substantial presence test yet) you can file Head of Household even if you live together if you have another qualifying dependent (as she can't be your dependent for this purpose.)
If she's eligible for a Social Security number (SSN), you can't apply for an ITIN on Form W-7. Since you indicate that you're waiting for her SSN, I assume this is the case.
If you are certain you qualify to file Head of Household (because you have another dependent) then you do not need to list any information about your wife on your return this year if that is how you prefer to file. If you'd rather file Married Filing Separately, follow Vanessa's instructions above (checking the box for Nonresident alien) and indicate that you do not want to treat your wife as a resident for tax purposes this year, then try to e-file. If the e-file is rejected, you'll need to file by mail.
You may benefit from waiting for her SSN and filing a joint return, and extending your due date as Opus 17 describes above.
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