The security built into your Mac is preventing you from doing this. In order to launch the Minecraft Server, try and launch it and get the error dialog above, and click the "OK" button. Then go into "System Preferences..." by hitting the Apple logo in the upper right of the screen, and then go into "Security & Privacy". You will see this screen:
Hit the button "Open Anyway" to open theMinecraft server jar (a dialog will come up, hit "open"). Once you do this that .jar file will now always open with no prompting. You can also change this behavior by twiddling with the radio buttons above to select "Mac App Store" or "Mac App Store and Identified developers" or "Anywhere". As you can see I have it set to "Mac App Store" and I will choose on a case by case basis; this is safest.
Minecraft will create a bunch of files in the directory in which the .jar file is placed, I would recommend creating a new directory and moving the .jar file there before starting it. The most imporant of these is the "server.properties" file, it is here that your daughter can change how this game behaves. Additionally, by invoking mincraft this way you allowcate the default amount of memory to the server, this may or may not be enough. There are reams of tutorials on how to tweek Minecraft server elsewhere on the web, enjoy!
Good Luck!