There are many examples of organizations created to support open source software: the DSF (https://www.djangoproject.com/foundation/), the ASF (https://www.apache.org/foundation/), and the GNOME Foundation (http://www.gnome.org/foundation/) are a few prominent ones. Are you sure you need this level of formality at this point, though? This carries a certain amount of overhead, and if you mean 501(c)(3) when you say "non-profit", it's a long process that may not go well (http://blogs.gnome.org/jnelson/2014/06/30/the-new-501c3-and-...).
It sounds like you're talking about a relatively new project with a small number of contributors. Would it be possible instead to make an arrangement with the core developer(s) to support the project financially? You may be able to structure this as a normal contractor agreement or via services such as Gratipay (https://gratipay.com/, formerly gittip) or BountySource (https://www.bountysource.com/). This would allow you to contribute while deferring the overhead of an organization until there are more people and resources involved.