Emily,
My daughters are 18 months apart, and big sister Kayla was all over little sister Hannah at first. When it's was all new. We did give Kayla her own baby and everything she would need when Hannah was born. I had it at the hospital and gave it to her with it's own baby carrier and diaper bag, and the day we brought Hannah home, Kayla brought home 'her' baby. Then at home when I took care of my 'baby' she took care of hers. It helped keep her busy and not always in Hannahs face.
And when she realized Hannah was STAYING and not just visiting, she didn't want that much to do with her<img src="i/expressions/face-icon-small-smile.gif" border="0"> It was really fun until this little person starting taking up too much of mommy's time and then she kind of did her own thing and wasn't always trying to kiss on her.
Hope it helps. And your baby is beautiful!! Congratulations to your family!