Whisper fails to correctly transcribe dementia speech because persons with dementia (PwDs) often exhibit irregular speech patterns and disfluencies such as pauses, repetitions, and fragmented sentences. It was trained on standard speech and may have had little or no exposure to dementia-affected speech. However, correct transcription is vital for dementia speech for cost-effective diagnosis and the development of assistive technology. In this work, we fine-tune Whisper with the open-source dementia speech dataset (DementiaBank) and our in-house dataset to improve its word error rate (WER). The fine-tuning also includes filler words to ascertain the filler inclusion rate (FIR) and F1 score. The fine-tuned models significantly outperformed the off-the-shelf models. The medium-sized model achieved a WER of 0.24, outperforming previous work. Similarly, there was a notable generalisability to unseen data and speech patterns.