Personalized text-to-speech (TTS) aims to clone the target speaker in the synthesized speech, imitating both the voice and speaking style. Current large language model (LLM)-based TTS methods ignore the style-specific prosodic patterns in generated speech, resulting in deficient style learning and thus limiting speaker similarity in synthesized speech. To this end, we investigate the prosody learning conditioned on the synthesized speech, and propose to predict the prosody of the current syllable based on previously predicted speech. Experimental results obtained on three datasets demonstrated the efficacy of the proposed dynamic prosody prediction method in enhancing the prosody learning capability, thereby improving the speaker similarity of the generated speech. Audio samples are available at https://muzw.github.io/dynapros/.