Ava and Sophia will be the ones deciding on the final design. They said they want something that's "fun and with a rainbow".
I added their comments on the logos they liked above. Hope that helps......
Update: Thank you, everyone, for the submissions so far. Here is the general feedback I have received from the girls so far:
1. They get a little confused if the submissions have a unique background colour (like black or yellow). They think it's part of the design. An all white background would help them to focus only on the logo.
2. The designs they have been most attracted to are the ones with caricatures included such as graphics of little girl heads, or clouds with faces. Further to that, they are generally drawn to less complicated and less busy logos (relatively speaking).
3. There is one logo of text with a rainbow that they kind of liked, but were otherwise not particularly drawn to logos that were text with a rainbow arching over the text. They didn't think such designs were "fun enough".
Also, this being my first time, I'm not sure if I need to explicitly state this, but just to be safe, I should note that the final image needs to be a vector based file.