I don't know of a reason why filing for divorce in the US would be a problem, as of itself it would not affect your immigration status. I have not researched the issue in depth, so if you need to be absolutely certain check with an immigration lawyer who has done so.

I don't think any state would regard a tourist as a legal resident (i.e., having established domicile), although I believe you are correct that Nevada will allow a divorce to somebody who is not domiciled in the state if they have merely resided in the state for six weeks (suggesting presence as opposed to legal residence / domicile). Recall also that your husband will need to be served with divorce papers, and be given time to respond to your complaint for divorce. You should consult a Nevada divorce lawyer about your plan, to confirm that it is possible and to get an estimate of how long it would take to get a divorce judgment.

A K-1 visa permits you to enter the United States for the purpose of marriage, and requires that you marry within 90 days of entry.