Yes you can pick that numbering style from the "multilevel numbering" button on the Home tab > Paragraph group.
The numbering level is controlled by tabs. Add a tab to move down a level, delete a tab to move up a level.
Why are you concerned about "losing bullets and formatting"? There may be something else going on.
Actually, if your kids can use word, it should be easy enough to teach them how to use outline numbering.
If they are old enough you may want to consider showing them the Outline view. When you use the built in heading styles and turn on outline view all of the text is hidden so all you see is the headings. You can customize the headings to use any number style
so that the outline looks exactly like your sample. As well, when you are in outline view, you can drag the headings to move them and the text under them to new positions. It is great for reorganizing an outline.
PS: did you know can do the same in the Navigation pane (formerly Document Map), that is drag headings around to re-organize the document.