I agree....address her need for reassurance. In my opinion, the fact that she's reaching for you at all is awesome! She's established you as a source of comfort and trust so, to me, it looks like you're well on your way to transitioning anyway. Once that occurs, the rest is pretty easy to sort out. Once a child starts recognizing me as their source of comfort, I do give them a little more physical contact and personal attention than the others. Many activities that we do will be done with the new child either on my lap, right beside me, holding my hand or just in very close, physical proximity. They need this to develop their sense of security in a new environment. Before you know it, she'll start 'anchoring' - wandering away, then coming back to check on you, going further and further each time. It is explained at all intake interviews that this is my method, it's been successful and EVERY child entering this daycare gets that benefit/luxury. The others will be fine in the short term. I find, often, that the kids who have been here longer, often will try to help make the new child feel better. It's actually a good way to develop empathy in young children. Incorporating a few circles into your week where you talk about feelings is also helpful. I'll do more 'Cuddle Puddles' at these times too, as they involve all the kids and it's just a fun way to show affection to everyone at the same time.
I don't know if that helps you at all. I know transitioning is a little slice of hell for everyone....not my favourite part of the gig either. But if I find if I just turn my thinking around a little, it's very beneficial and makes the process more tolerable.