Yes. Your understanding is correct. You can file as married filing separately and since your spouse does not have US income and is nonresident alien she would not need to file a US tax return. Next year you could file a joint return.
Further, the better option may be for you to file as head of household since you have dependents. Here is a link with more information.
Any dependents you list on your return need either a Social Security Number (SSN) or Individual Taxpayer Identification Number (ITIN). NOTE: If you file as married filing separately the same rule applies to your spouse. Here is a link for reference.
Finally, here is a link with information on applying for SSN or ITIN. You will need to do so for either your spouse or your dependents depending on your filing status.
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