Hi, i used to work in nurseries, but now have 3yr old of my own and realise how hard it was for all those parents leaving their children with me! .
I won't lie to you, 9mths is a tricky age, because many children are just beginning to become aware of surroundings and 'strangers' and realisation that a parent has left the room. Of course your dd may not have this phase or may of already been through and out the other side.
I'm only telling you that just to prepare yourself for tears. What can be quite common is that for the first few days children are all happy and smiley thinking this new environment is great, waving mum off no probs, but on say day 3 or 4 the reality hits that its permanent and they may decide to yell when they realise you're going to leave them again. Make yourself prepared for this - it does not mean the nursery are doing anything wrong, just reality hitting home with child.
I would advise staying for one or two sessions, and then leaving her for short periods, gradually making that time longer each day. Stay firm and stick to your plan, so if you've started leaving her and then she cries, don't decide to stay again as will just give her expectations that you won't be able to keep the following week.
I always welcomed parents to stay in the building, just out of sight to make them feel more comfortable, and also encouraged them to ring in in the early days so we could reassure all was well.
If your dd does cry, the chances are it will be short lived. That inital watching you leave might make her cry, and then once she is distracted by other children and new toys, she will enjoy her day without you!
Sorry this is so long! You are not alone in feeling tearful, most of us do, but give it a week or two, and it will become second nature to drop your child off and you'll start to enjoy time to yourself again (i know its work, but i consider that time to myself also ).
Good luck x