Great idea! I use a commercial bottle tree, and it has a base that is much bigger than what you have, and still threatens to tip over if I pull the bottles off of one side. Either be very careful how you use this, or add a wider base, or both.
I just used screws to hold the pegs (just put the PVC over the screws). As far as stability is concerned, I've had 40+ bottles on it already with no stability issues. Fingers crossed that this continues! I think I have the pegs evenly balanced on all for sides to prevent toppling. I think that if I were to add a rotating base, the stability of the entire structure would be compromised.