Make a vector graphics version of my avatar from low-resolution image

I use an avatar for very long time, it was designed using vector graphics package, but now I only have low-resolution version of it. I need you to convert it using automatic tools, or draw it again using low-resolution image as a guide. It should be as cute as it is now :), and use exactly that colors, but be in vector format, so I can print (or export to PNG, with transparency) huge versions of it. I do not know what is the best vector format (SVG? Photoshop? Corel Draw?), you should tell me what is the best one and why.