What can I do if my advisor threatens to take away authorship of my undergraduate research work?

If you are the original author, you have authorship rights and your advisor cannot take that away from you. The worst that she can do is refuse to coauthor with you and take her own name off the paper, not yours, although if she did that, you should remove her contributions from the paper.

At your school, there should be a number of people who will advocate on your behalf, and I would start there. The dean of students and the department secretary are usually good first stops. If that fails, you could consider going to the school dean, the provost, or conceivably even the university president (although if it got that far, you are likely in the wrong or have a terrible program). If your advisor publishes without you as a co-author, you can seek redress with the editor of the journal where she publishes.

If you already know that this is an issue, you need to start getting your "ducks in a row." A first step would be to 'publish' your paper as a working paper somewhere. Where you do that is going to be discipline specific, but SSRN is a good choice if you are in the social sciences, and Academia.com has this ability as well. If you do that, make sure you give appropriate credit, too. Two wrongs don't make a right, as they say.

Try to ensure that as many people as possible can attest that the idea is yours, and if you still have the original graded by the professor make digital copies, preserve the original at all costs. In the end, you don't want it to be your word against hers, and the more evidence and witnesses you have, the better. Rightly or wrongly, other faculty are more valuable than students, so show it to as many faculty as possible.

A few words of warning.

1. What you are talking about is plagiarism, and could even be intellectual property theft. Universities take this very seriously, and it can end careers—both yours and your advisor's. Consequently, things can get very dicey very quickly. Be absolutely certain before you start making claims publicly that you are in the right: talk to someone you trust outside the department and outside the discipline and show them your work with the work you are doing jointly with your advisor; verify your sources; know your allies. Once this goes beyond you and your advisor, and perhaps a small cadre in the department, it is the intellectual equivalent of going to war.
2. Be prepared to come to the table. If this isn't published yet, then there is still hope for a negotiated solution. Know what your objectives are, and use your position to get those objectives, and don't get hung up on abstracts. For example, if you are really hoping to get into law school, then being author may not be as helpful as something else, and be prepared to accept that something else. Make no mistake, what I am talking about is corruption, but as an undergraduate, it is highly unlikely to be worth hanging yourself out to dry over something like this, if there is a negotiated compromise. On the other hand, if you are hoping for a PhD and a career in the field, then authorship can be crucial, and you may need to go to the mat over this so as not to be seen as a pushover or a flake in the future.
3. Don't get caught up in office politics. If your advisor has enemies, and she likely does—especially if this is typical of her treatment of others—departmental enemies will likely try to use you as a weapon to get to her. While it may be gratifying to do so at first, if you let that happen your interests will fall by the wayside as the whole issue becomes about whatever stupid issue is driving the office politics, and not about your intellectual and students rights.
4. Don't get steamrolled, but don't overstate your contribution. This is hard as an undergraduate, because you definitely don't have as much information about the discipline as your advisor, and it can be tempting to think "My idea changed the world!" whereas it is only a minor contribution. Know what you have done, and don't get pushed off that, but being seen as someone who is self aggrandizing or consistently over-estimates their own importance will hurt your cause. There are already people who devalue contributions because of who the contributor is, and you don't need to give them any ammunition, or give your potential allies pause because they are unsure of the reliability of your perceptions.