Ph.D. student in Biology-Neuroscience Concentration here.
First, if you are interested in applying to Neuroscience graduate programs, it's good that you have a solid technical background with a degree in chemical engineering. Scientists in biology/neuroscience highly value technical skills and aptitude, especially when quantitative and analytical methods are critical in lab work nowadays. Potential principal investigators would deem your background favorable.
Second, I wonder if you have any experience in neuroscience research, or am planning to either start an internship or a research assistant position in a neuroscience lab. I think it's common knowledge that before entering a Ph.D. program in a specific field, it's important to gain some hands-on experience in the field. (M.S. would be generally slightly different because their selection is not as competitive as Ph.D.). Also, I think it'd be good to have at least one recommendation letter from a neuroscientist who can attest to your abilities and potential as a researcher.
So, in conclusion, it seems like it'd be good for you to apply to work in a neuroscience lab first and gain some hands-on experience before applying for Ph.D. programs. If you'd be interested in start applying later this year, it'd be good to start working in a lab pretty soon so that you can at least gain several months worth of experience. I'd say that in your case, applying next year or so might be more realistic. Also, I'll say that taking online classes might help but would not be sufficient in building up a strong application.
I also recommend emailing professors/researchers whose reearch interests align with yours and asking them for a video conference call to talk about your future plans, what sorts of graduate students they are looking for, etc. It'd be also good to ask whether they are looking for a research assistant, lab manager, or a lab technician in their labs, so that you can possibly fill a role.