I'll return to the OP's questions, without judgment.
Most employers will not share the exact reasons for termination when a new, prospective employer requests a reference. Many people believe there is a law that forbids this, but it's more the threat that the employee will sue for defamation that prevents employers from sharing the details or reasons an employee left or was terminated. So, officially, your employer will state, "Mr. Smith was employed here in the capacity of an RN from August, 2012 to January 2013." That will be the extent of what they state in writing or by email--but, if the manager where you are applying calls her friend, the manager where you were dismissed, the 'off the record' details may be given. So, you're taking a risk if you claim to have left voluntarily and they find out otherwise. They will likely assume you've been terminated (even if they don't know the details) because you are applying for jobs while not currently employed (few people quit a job before securing a new one).
It's very likely the next move is termination after suspending you. Employers are careful to dot their i's and cross their t's before firing an employee. They don't want to be in a position where they are forced to rehire, pay unemployment, or lose a lawsuit. This is the reason people are first suspended then days or weeks later they are terminated. You might choose to resign as you could legitimately state on future applications that you quit, rather than have to say you were fired. (But, again, the truth has a way of coming out--honesty is virtually always the best policy.)
I have no idea how long you've had this job--you state it's your first job--but if you were there less than 6 months or even a year, you may simply choose to ignore this on your resume. One of my duties is hiring employees; I might be reluctant to hire someone who was terminated for what you did, but I'd also be hesitant to hire an applicant who graduated a year ago and has no nursing experience. Either way, your options aren't great. Unfortunately for those with less-than-perfect records, there is a lot of competition for very few nursing jobs. Employers can afford to be selective; with all things being equal between two applicants except one had a lapse in judgment and the other didn't, guess who will get the job?
My best advice is to resign, put your resume together (considering whether you think admitting to this is better or worse than having no work experience) and cross your fingers. I cannot predict how other employers will react; hiring managers are people, and people are individuals with very different standards and values. What one person believes is a youthful mistake, another will think is a terrible lapse of judgment (and not be willing to risk hiring someone who might make other bad decisions).
Your career may not recover from this (especially with the surplus of able and experienced nurses seeking jobs). I'm not trying to be harsh, but I read many of the replies to your original post and suspect you might have what employers call 'attitude problems'. You do accept responsibility for your actions--which is very admirable and mature, but some of your other comments come off as hostile and argumentative. It could be that you're stressed over this situation, which is understandable. But, for your sake, try to tone it down a notch or two. You'll be more employable and more respected by your colleagues and managers if you don't take the offensive when you don't agree with what others have said. Good luck.