If your wife does not need a visa, she may come here as a tourist provided that she has not already spent 90 days in the Schengen area. She may then stay in the country while her application is processed.

If your wife does need a visa she cannot come to Iceland until her permit has been granted since visas are not issued for this purpose.

Keep in mind that if she does not have a health insurance in Iceland, you must pay the medical costs that result from the birth.