Welcome to the board... To answer your question correctly, how old is your credit file? And which Credit Union were you thinking of getting a loan from?
I would recover from the incurred debt before going out and buying a new car.
Im not saying you don't deserve a new car, but I don't get the point of having to have something new while you currently hold 50% DTI? Even if you were planning to use the auto loan for some type of debt consolidation, Id still consider passing on it.
Opinion aside, yes your credit union will look at your DTI. Will it kill your chances? Most likely not - but are you sure the 125% is available for all? A lot of times those "bonus" terms are only reserved for people with excellent credit.