Sure you can, just export your canvas to JSON
var canvas = new fabric.Canvas('c');
data = JSON.stringify(canvas)
Now you can send that data using a post request or store it in a database or whatever you want.
canvas.loadFromJSON(data, canvas.renderAll.bind(canvas));
Example: http://jsfiddle.net/P9cEf/3/
The example uses two canvases one page, but the concept is the same.
Edit: To download the image client side
var canvas1 = document.getElementById("c");
var image = canvas1.toDataURL("image/png").replace("image/png", "image/octet-stream");
window.location.href = image;