Dawno, I would honestly say that only do this if you really feel it is by far the best solution for your child. You're the one who will be leaving her so you must feel strong about it.
My personal view is that you are doing fine taking her to playgroup. If you do that and maybe one other mother and toddler thing a week I think that's perfect for a 15 month old. I think sometimes people seize on them being with other children a lot as a solution but in fact being with you and watching YOU interact with others is also very valuable to her - seeing you talk to your friends is role modelling to her how people are in the big world and it is from this that she learns how to interact. When the times comes and she herself is interested in playing with others, she will have a good solid grouding and understanding from having watched you and been gently guided by you at playgroups. Much easier o her I think than 'in at the deep end' on her own.
One major thing I have learned about kids is that 99% of it is about 'readiness' - they can't do things until they have the mental and emotional readiness; by this I mean that Nursery would give your daughter experience of being around groups of kids but that won't actually give her the ability to relate to them any differently until she is ready; children play 'alongside' rather than with eachother sometimes up to about four years old, and I know children who still find it very difficult to share at older than this and when they have been attending pre-school or nursery daily!
I peronally think relax, enjoy life with her and let her get her first experiences of other children with your guiding presence comfortingly near.
My own experience was similar to you, and I also felt pressure from friends who did use Nursery to send him - they said similar things to Janos who says her DS doesn't look at her when dropped off and gets upset when he has to leave nursery. I'm glad that she feels happy with her arrangements and I'm sure her DS is fine - but it is not obligatory for a child to be happy to leave it's parent at this age and it is NOT an indication of problems if the child does not 'practice' leaving the parent at this age. I'm sure some of my friends thought my DS would be clingy because he hadn't had nursery. However he now attends preschool two mornings a week and has settled absolutely fine, enjoys it and is no more clingly - in fact less so than some who have done nursery. It's all about readiness.
I am glad that unlike some of my friends I never had to leave a sobbing child at nursery - some had to bear this for MONTHS while their child adapted. My DS and I have not had to go through this and he is coping as well if not better with socialising than some other children. So the point of my rant is DO WHAT FEELS RIGHT TO YOU! and don't bow to any 'pressure' from others.