I think Unwashed forgot to add the thread.
Yes a constitution should be made.
It is a pretty simple thing to compile, I suggest you obtain a constitution or two from other organisations and look at how they are drawn up first then draw up your own.
The constitution should be registered with your council.
They should be able to advise you too.
Once you have a registered constitution you have a status and this can mean that you can apply for grants and other things.
The constitution should briefly show what you are and who you are. Your intentions and aspirations. It is a good idea to mention that it is "non profit making" organisation too.