Can I transfer Minecraft from a computer to iOS?

I'm afraid this is not possible. Minecraft for the PC and Minecraft: Pocket Edition (for tablets and phones) are two seperate games. In order to enable your son to play on the iPad, you will need to purchase Minecraft PE from the app store, and he will not be able to play in the same world he has on the PC.

You can port maps from the PC with very little differences...

Blocks that exist in the PC version will NOT be transferred over (such as command blocks).

Here is a very good tutorial on how to port maps:

Please note that you will have to buy the FULL version of Minecraft Pocket Edition. You can use iFUNBOX to browse the file system of the iDevice.

Your device does not have to be jailbroken.