I have a job at a non-profit.

I get paid.

cool thanks for heads-up!

Supporting a non-profit isn't the same as being anti-profit. I think it would be a great opportunity to expand the community and would increase competition. Let's face it, MtGox could use some.

Based on the volume over the last couple of days, TH is giving MtGox a serious run for their money now.

Non-profits typically need to be incorporated in some way and are subject to government scrutiny.  Someone needs to be responsible for all of the back-end stuff and that someone will have legal responsibilities.  We've seen what happens when an exchange gets significant volume and only has a couple of staff.  You'd need to employ paid staff as well as attract initial funding to get it up and running.  It's not a bad idea but it needs a significant lead time to be executed well and some serious upfront funding.

would it be possible to make something (p2p application) that would be distributed on miners computers ?
they would host it , and through that network to run the exchange

False. The (theoretical) absence of charities would still fail to justify violence against peaceful individuals.

The only "laissez-faire advocates" that are unable to further their arguments in the absence of charities are those that haven't based their conclusions from first principles. When you work from first principles, the conclusions don't matter.

How would you transfer the dollars?