doc: Add in novel Drake images for newer website (RobotLocomotion#14613)

doc/images/drake-dragon.README.md

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+This SVG does not render well in Firefox (nor in Inkscape), so we rasterize it.
+
+Steps used to generate the accompanying PNG:
+
+```sh
+# For Ubuntu 18.04.
+sudo apt install inkscape imagemagick-6.q16
+
+cd drake/doc/images
+# Export with inkscape.
+inkscape --without-gui --export-area-drawing --export-dpi=300 \
+    drake-dragon.svg -e drake-dragon.png
+# Scale down with ImageMagick.
+convert ./drake-dragon.png -resize 25% -strip ./drake-dragon.png
+
+# Generate favicon.
+convert ./drake-dragon.png \
+    -resize 200x200 -gravity center -background none -extent 200x200 -strip \
+    favicon.png
+```
+
+*Note*:
+I (Eric) tried 96 and 150 DPI. Did not look great.
+
+I also tried stuff like
+```sh
+convert -units PixelsPerInch ./drake-dragon.png \
+    -density 300 -resize 800x800 drake-dragon.png
+```
+but it looked bad.

doc/images/favicon.README.md

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+Two different files at the moment.
+
+- `favicon.ico`: This is the original website.
+- `favicon.png`: This is for the new website, converted per
+`./drake-dragon.README.md`.