How about using an image management application instead?
I use iPhoto and I hardly ever bother with the name of the images. Instead, I use keywords and have made a keyword (or phrase) for each person in my family, my friends, and even myself. I also use keywords for groups such as "family" or "classmates".
I've made lots of keywords or phrases, and it's so easy to select a lot of images and then click on a keyword to have it assigned it to all of them at once. The keyboard shortcut for the keyword window is in the Window menu, and is Command-K. There's even a quick group of keywords that you set up when editing the keywords. That you just press a key (your choice) on the keyboard to assign the keyword when the keyword window is open. Pressing the key again will remove the keyword from the selected pictures, just like clicking on the keyword.
From that, I have made Smart Albums based on the keywords. For example, I have Smart Albums for some people in my family and an overall Smart Album for the "family" keyword, too. The albums can also be grouped into folders within iPhoto, and therefore selecting the folder will reveal all the images in all the albums in that folder.
So how does that help if sometime later for some reason you need to use the photos of your daughter, and you need them numbered sequentially for some other reason? Well, you can export selected images or a whole album (none selected) and it'll give you the option to have them renamed sequentially. No fancy options, just the prefix name, so if you want a space or a dash then be sure to include it at the end of the name. When exporting, they are just copies of the images still in iPhoto, but they can be exported in a different format, a different quality, and even a different size.
So, I guess the question to really ask you is "Do you really need to have them named sequentially, or just on rare occasion?" iPhoto seems very nice for managing my photos and with nice export options. Though, I usually just drag and drop copies out of iPhoto when I need them, it's not often I need a large amount exported. It also keeps me from having to deal with them in the Finder, so I never bother with them except through iPhoto since it's so much easier. iPhoto is like the Finder, but specially made for managing photos instead of generic files. A lot like iTunes is specially made for managing audio and video instead of generic files.