>>129A constitution? No. There would likely be many contracts people would have the option to accept or not, but they would not constitute statutes that apply to everyone (or else it wouldn't be anarchy). Due to that, there can't be IP because you can't impose your monopoly without imposing laws and thus nullifying the state of anarchy.
Laws? Absolutely. Tons. You get all the laws you can buy, but again, remember that this doesn't oblige anyone to obey them. Laws would naturally take on their more traditional role of dispute resolution rather than serving as commandments.
It's generally safe to say "I don't know" when discussing anarchy, though. The fact that we don't know the ideal way to organize society is kind of the point of anarchy. You have to try lots of things at once and let people adopt what works for them.