I think you must remove the white background and the margin and choose a good font that fits with the flower. I like the flower very nice
The only thing i'd suggest would be to change the font on the link of text at the bottom, to something simpler, Helvetica light perhaps.
I would make the letter 'z' the same size as the other letters. Also, what niche is your friend's site? That's a pretty important factor to consider if we are to grade the quality of your logo.
Its cool, maybe a little more color though...ad some shading too, maybe make the letters have a 3-D like appearance.