Pre labor!!!

I found out two days ago (at exactly 34 weeks) that's I am 1 cm dilated and half thin. I went to the Drs because I thought I was having contractions, which I very well was. Once realizing I was dilated they sent me straight to the er to get better tests done. They told me that it wasn't unheard of and they won't stop my pre mature labor but if she comes before 37 weeks they will have to give me a steroid to help develop her lungs so that she can breath on her own once she is out. & just this morning my mucous plug went! Has this happened to anyone else? 34 weeks seems very early to have her! But the Drs say she is in beautiful condition so there isn't anything wrong with her. Just eager to come out I guess?