A current limit in power scaling of Yb-doped fiber amplifiers is the sudden onset of mode instabilities. We investigated this effect on a single-frequency Yb-doped photonic crystal fiber amplifier with a low mode instability threshold power. By measuring the overlap of the fiber output beam with the fundamental mode of an external cavity to be about 95\%, we could exclude significant modal power transfer below a sharp power threshold. Furthermore, we directly measured the frequency resolved intensity noise spectra. No fluctuations in the overall output power were observed, but for the modal content different oscillation regimes were identified.