Zheng, seeded six, won 6-3 7-5 (7-5) against world number 80 Doi on another rain-affected day on Friday to set up a clash with compatriot and top seed Peng at the WTA 125K Series hard-court event in Nanchang.
Doi struggled with her serve and won only 59 per cent of points on her first serve as she was beaten in two hours, five minutes.
Zheng is 152 places below her opponent in the world rankings, but rose to the occasion on home soil as she took three of the eight break points that she manufactured and held her nerve to see out the match in a second-set tie-break.
The 20-year-old can now look forward to a clash with Peng, who reached the last four courtesy of an emphatic 6-2 6-2 victory over Wang Qiang.
Wang won 63 per cent of points on her fellow Chinese player's serve as she coasted into the semi-final in just one hour, 11 minutes to live up to her billing as top seed.
Luksika Kumkhum is the only non-Chinese player remaining in the tournament after she accounted for Wang Yafan 6-4 7-5.
The fourth seed from Thailand was made to work by world number 333 Yafan in an error-strewn encounter in which Kumkhum prevailed despite double faulting 10 times compared to her opponent's eight.
Fangzhou Liu stands between Kumkhum and a place in the final after she beat Ling Zhang of Hong Kong 6-1 4-6 6-2.