The small company I work for values profits over quality. Is this company doomed to fail?

Yes, you should. You can compare this organization to the 2007 housing market bubble. The organization might make some short-term gains by ignoring quality, but eventually everything will come crashing down. It's possible your boss might even be positioning you as the scapegoat when everything falls apart. Get out of there as soon as you can.

Bruce, it never hurts to remain current, explore options, and expand your footprint in the industry. To be quite honest, based on your posts, the answer seems quite clear :)

The process to find a new opportunity can be lengthy. It is much easier to navigate while employed.

I agree with my colleagues here.
You should try for a better opportunity while you are employed, so go for it and good luck.

I agree with other posters here. From your posts you sound very unsatisfied with this organization. The culture is clearly not for you and you seem to feel you have some power struggles as the PM.

Continue working there, explore your options, and make the move. I can tell you are instinctively ready to move on. Don't burn bridges, continue to deliver your best, be motivated, come with the same energy and show up each day. You will be a superstar to the right fit in the future. Your heart is in the right place, but don't try to over lead with your heart. It will lead to frustration and self sabotage.

Hope this helps and makes some sense to you.

Quality is suggestive, but you can't go without delivering a level of quality that is acceptable to the client.

Agree with other comments, look for a better company.