Although a macro would be more re-usable, you could do this without macros relatively quickly if you carry out the following steps.
Change the Outline View and show only headings 1-7
Select all and click the Change Case button on the Home tab to set a capital letter on each word.

It is also possible to do a series of search and replaces for the preposition handling but it is not simple because any heading that starts with a preposition should probably retain the capital for that particular word. However, a search and replace on the selection (don't continue for rest of document) will just do the headings when they are shown and selected in outline view.

Someone might supply a macro to help you out but the above instructions will let you get most of the way there without a macro.