save yourself some trouble and go ahead and get the infant car seat. your little one will not be able to sleep in a convertible car seat and it is so much easier--especially in those early days--to just lift the car seat out of the car than to have to keep buckling and unbuckling an infant in. I remember NUMEROUS times that my DD fell asleep in her infant seat and we were able to just bring it in to the house where she slept another hour or two. Once we changed her to a convertible seat, that ended pretty quickly.
Some kids outgrow the infant seat quickly, others stay in it awhile. My DD is a peanut and she was in it until nearly 18 months. We definitely got good use out of it and will be using it again with our next.
As someone else already posted, infant seats are much safer as well.