Will my Community college engineer transfer plan work?

Realistically, most four year schools admit transfers to start in the fall, so you would target fall 2016. Recommended courses before then:

Fall 2015: Physics 235, Math 209
Spring 2016: Physics 236 (and 237 if needed for your major at the four year schools), Math 210

Your major may require some CS courses. Check the four year schools to see whether Olive Harvey CIS 103, 116, 142, 144, 244, 250, 255 can be applicable.