"I will do it"

It indicates that it's a single action and it will happen in the future.

"I will be doing it"

It also indicates that it will happen in the future but it's a continuous action. It's often accompanied by another action.

For example: "When you arrive at home, I will be watching tv"

Notice that this action is happening at the exact moment the other person arrive at home, it's not a general action.

Hope I could help!