Higher repetition-rate optical pulse trains have been desired for various applications such as high-bitrate optical communication, photonic analogue-to-digital conversion, and multi-photon imaging. Generation of multi GHz and higher repetition-rate optical pulse trains directly from mode-locked oscillators is often challenging. As an alternative, harmonic injection locking can be applied for extracavity repetition-rate multiplication (RRM). Here we have investigated the operation conditions and achievable performances of all-fibre, highly tunable harmonic injection locking-based pulse RRM. We show that, with slight tuning of slave laser length, highly tunable RRM is possible from a multiplication factor of 2 to >100. The resulting maximum SMSR is 41 dB when multiplied by a factor of two. We further characterize the noise properties of the multiplied signal in terms of phase noise and relative intensity noise. The resulting absolute rms timing jitter of the multiplied signal is in the range of 20 fs to 60 fs (10 kHz-1MHz) for different multiplication factors. With its high tunability, simple and robust all-fibre implementation, and low excess noise, the demonstrated RRM system may find diverse applications in microwave photonics, optical communications, photonic analogue-to-digital conversion, and clock distribution networks.