They aren't all under 1KB, but there a few repos on GitHub hosting all of the Font Awesome icons as SVG.

Also, if you can avoid it, don't use <img src… to display SVG images, as the article suggests. By using <svg… directly, you avoid extra requests, you gain the ability to manipulate them directly in the DOM, and to restyle them.

https://github.com/ivanvotti/font-awesome-svg/tree/master/SV...