I feel strongly about this thread...it deserves more attention.
I'm pretty sure it's illegal to fire you simply for having depression and no other reason. It would be legal to fire you if you pulled a bunch of no-call, no-shows, or even were constantly calling out with excuses when the truth was you just had no energy to go to work.
But simply for knowing that you have depression? No. In other words, just try not to let it influence your performance on the job. Also, the simple fact that you are going to a psychiatrist/counselor does not tell your employer that you have a mood disorder. People go to counselors for temporary reasons, too.
elkpark is right; no one at work needs to know, except of course you're not allowed to lie about it if you are officially asked a direct question. (I'm not sure I see that coming up, unless someone notices that you seem depressed and asks if you are seeing anyone about it.) If you don't tell them and they don't ask you, they are likely not to find out.
Also as elkpark mentioned, MANY health professionals across all fields are seeing counselors, psychiatrists, and other professionals AND are taking medications. Nursing and health care in general is a stressful job, so the need for some kind of help is very common.
In fact, I don't know where you work or how many people are there, but you might be surprised at who among your coworkers is getting psychiatric help. If you know a good assortment of people, chances are someone is.
It's been over a week. I hope you've taken action by now, but if you haven't, I would really encourage you to do so. A really good
therapist is completely invaluable. It can be a pain finding one you really "click" with personally, but when you do, it's so helpful. Some therapists will ignore you and prescribe medication and have you out of the office ASAP, but I've met some who are just wonderful to talk to and really help you work on the things that bother you. Of course, they'll prescribe meds, too, if they believe it is necessary.