I recently built a mind mapping tool using fabric.js and I encountered the same problem. 
To achieve what you have described (changing the text on and after creation of textual elements in the canvas), I used jquery to detect the keydown event. Assuming you have selected the desired textual element in the fabric canvas the following snippet will change the text.
$(document).keydown(function(e){
    var keyPressed = String.fromCharCode(e.which);
    var text = canvas.getActiveObject();
    if (text)
    {
        var newText = '';
        var stillTyping = true;
        if (e.which == 27) //esc
        {
            if (!text.originalText) return; //if there is no original text, there is nothing to undo
            newText = text.originalText;
            stillTyping = false;
        }
        //if the user wants to make a correction
        else
        {
            //Store the original text before beginning to type
            if (!text.originalText)
            {
                text.originalText = text.text;
            }
            //if the user wants to remove all text, or the element entirely
            if (e.which == 46) //delete
            {
                activeObject.element.remove(true);
                return;
            }
            else if (e.which == 16) { //shift
                newText = text.text;
            }
            else if (e.which == 8) //backspace
            {
                e.preventDefault();
                newText = text.text.substr(0, text.text.length - 1);
            }
            else if (e.which == 13) //enter
            {
                //canvas clear selection
                canvas.discardActiveObject();
                canvas.renderAll();
                canvasBeforeSelectionCleared({ memo: { target: text} });
                newText = text.text;
                stillTyping = false;
            }
            //if the user is typing alphanumeric characters
            else if (
                (e.which > 64 && e.which < 91) || //A-Z
                (e.which > 47 && e.which < 58) || //0-9
                (e.which == 32) || //Space
                (keyPressed.match(/[!&()"'?-]/)) //Accepted special characters
            )
            {
                if (text.text == text.originalText) text.text = '';
                if (keyPressed.match(/[A-Z]/) && !e.shiftKey)
                    keyPressed = keyPressed.toLowerCase();
                newText = text.text + keyPressed;
            }
        }
        text.set({ text: newText }); //Change the text
        canvas.renderAll(); //Update the canvas
        if (!stillTyping)
        {
            this.text.originalText = null;
        }
    }
});
Using this technique, I can select a text element in the fabric canvas, begin typing and the text is replaced. You could change it so it didn't erase the text each time you select the element.
There are some compromises with this method. For example you cannot select text as if it were in a regular HTML input text element and there is no blinking cursor, therefore the "virtual" cursor is always at the end of the text.
If you really wanted to you could draw a blinking cursor at the end of the text.