My little one needed those often during her first 2 years. She has GI issues (feeding tube, etc) and she vomited to the point of dehydration and IV's a few times. The ped prescribed the suppositories and I had a supply at home. After I got those, I only had to take her to ER one more time. Those things worked to keep her home and for that I'm grateful.
I'm sorry your baby is vomiting so much.
If she's somewhat active still, talking, crying tears, moist lips, and willing to keep nursing, she's probably okay to stay home. Just keep pushing the fluids. You might even use a medicine syringe to give her some water, decaf tea, or broth in between nursing. Make sure to give her a little bit at a time, but do it often. This will help to prevent vomiting.
If you go to the ER they will most likely put in an IV right away unless you are very firm about them not doing it. If you don't consent to the IV they will wonder why you are there. They like to see babies hydrated because they can go downhill so fast when dehydrated. It's amost standard procedure to get an IV of fluids. I really doubt they will tell you to stop nursing. And if they do you can tell them your rights as a parent. They can't make you stop nursing.
If you would rather just have the suppositories and avoid an IV, I would suggest going to a pediatric urgent care center instead. If I had to chose between IV and suppositories on a child who was not severely dehydrated, I would choose the suppositories. Much less traumatic.