I began by importing the original PNG into Inkscape and made a lot of measurements. I used these to determine where each object would be located in relation to each other.
The original image was then used as an overlay in which I filled in the blue part, using a combination of circles and lines. Instead of keeping it all I decided on splitting it in half and using a duplicate for the other end. This way the right and left side of the blue were identical. If this lack of symmetry was intentional, changing it back should not be an issue.
The rest was quite simple. It mostly involved adding all the smaller objects based on the measurements and adding black strokes on the edges.
One thing I am considering is how I handle the text. Currently I use the "Create and edit text objects" tool and the Roboto font. Issues to consider is the license of the font (Apache License 2.0). It may not even be the best match against the original. I have not taken the time to look around for a better one yet. Another way to handle it would of course be filling it in by hand, based on the original, but this will be a bit more work and I am uncertain if it will scale as well.
The new icon is currently 512x512 px, but the picture itself has close to the same aspect ratio as the original PNG. If you stretch the original and make it transparent you will see that everything lines up quite well.
Imgur link if that is preferred:
http://imgur.com/a/TWM69
