Actually, your ex is correct, you don't have any 'rights' to say who he should introduce to your dd, or when - any more than he would be able to decide that for you. All you can do is explain to him how badly upset she was last time (did he not notice himself?) and ask that he consider her feelings before introducing her to this new girlfriend. It won't hurt to wait until he knows if this is a serious long term relationship or not.
What you can do for your dd is talk, allow her to express her feelings, reassure her that loss is a part of life, etc. If your dd is old enough, you might consider letting her attend Rainbows - it can be great for helping children deal with the all the different issues of parents who have separated.