Can I transfer a Dragonvale world between accounts?

According to the Android Device FAQ from Backflip, you can transfer a "local" park to be a "facebook" park, using the options menu within the game. A "facebook" park can be signed into from a different Android device (but not from an iOS device).

If you have an existing Facebook park, you'll be prompted to ask which park to keep. Parks cannot be converted back to local parks, and you can only have one Facebook park.

In Dragonvale, there are two modes of access: 1) local mode, and 2) server mode. For a user to use "server mode", they must connect to Facebook. If the user has played without doing so, their Dragonvale game information is stored only on local mode, and cannot be transferred. If the game was connected, then the user can access that park on any device, so long as the user installs the Dragonvale app, and then signs in to their saved server information by connecting to Facebook.

If your children signed into their Facebook pages, then their game is saved on the server, and they will be able to retrieve them. If they have not connected the game to Facebook, then they will not be able to save their park information, and will have to start again when they start playing on a new device.