Hi Stopster, welcome!
I doubt the diamond in the blog you linked would in any way be defined "blue". Possibly fancy grey - which is good news since the word "blue" in a diamond's colour tends to cause serious wallet cramps to the buyer. Fancy grey, on the other hand, are relatively cheap even in larger sizes, but they aren't very popular and thus not very easy to find.
The "smokiness" of the stone is largely due to a lot of inclusions - which again bring down the price, but may not be to everybody's taste. Getting a strong grey with uniform colour and lively is also not easy, since the inclusions need to be dense to provide the colour, yet not dense enough to interfere too much with light reflection. For example, that particular stone appears to be quite lifeless even though it has no big black inclusions (at which point, I'd rather have a blue chalcedony - but that's a whole other story).
On size, it's impossible to say. If the finger is a "normal" size 6 to 7, then it faces up around one carat; however the weight depends on a lot of things one can't see (namely the pavilion and the girdle of the stone), and it really cannot be guessed accurately. In any case, I'd say that what matters is what you see, not the weight, so just go for a stone that has a diameter of about 1/3 to 1/2 of your beloved's ring finger.
Same thing on "rose cut": cannot really say, but IF it has been rose cut the "rose" is pretty much invisible:
1) The visible part seems to have been cut just like a crown on a standard round brilliant, which is unusual for rose cuts - they tend to be flat on the part that is not cut into a rose.
2) Even if the pavilion is rose cut, the lack of transparency in the stone is such that any faceting effect is hidden - at least in the photos.
Where to find one is the tough question; I'm sure David (the sponsor of this forum and owner of Diamonds by Lauren) can get hold of "something like this", but the real issue is what is it "like": size, colour, cut, overall appearance? Which of these things would you like to or would you be open to change? I personally don't like the look of that diamond, even though I quite like the overall idea of the ring.
Finally, on buying online: I think it's perfectly possible on three conditions:
1. Choose your dealer carefully.
2. Get as much documentation (good quality photos, diagrams, whatever else can help you make up your mind, including expert advice) as you can.
3. Make sure you can return the item if it's not what you expect. From that point of view, it does help to see the stone loose before it's set, even though it adds to time and (shipping) costs.
In practice, it really boils down to the first of the three points above.