I sent my app in late July. Have heard back from MCW, South, and Indiana (3.7 GPA, 510 MCAT). You should ABSOLUTELY apply. Before you send it in, take a long hard look at your app. Your goal is to set yourself apart from other applicants. Own your "low" stats (your GPA is just fine) and elaborate in your personal statement/experience descriptions about how each experience made you into the person you are today and helped form your desire to pursue a career in anesthesia. Don't half-ass things. If you don't feel good about your app, don't send it in until you do. You have over 4 months still, the first round of interviews for the programs I listed above haven't taken place yet and there are therefore 0 accepted applicants at those programs currently. Other things that can help set you apart include BLS certification, presentations in a professional setting, and any time spent in a leadership position.
In all honesty, your MCAT score might hold you back a bit. I would think about taking the GRE to boost your chances and show your dedication to this career path. If you're in a position to wait another year to gain meaningful healthcare/research experience, I would give the MCAT another go instead. Good luck and stay confident!