A Fourier domain mode-locked (FDML) laser at $1050\mathrm{nm}$ for ultra-high-speed optical coherence tomography (OCT) imaging of the human retina is demonstrated. Achievable performance, physical limitations, design rules, and scaling principles for FDML operation and component choice in this wavelength range are discussed. The fiber-based FDML laser operates at a sweep rate of $236\mathrm{kHz}$ over a $63\mathrm{nm}$ tuning range, with $7\mathrm{mW}$ average output power. Ultra-high-speed retinal imaging is demonstrated at 236,000 axial scans per second. This represents a speed improvement of $\sim 10\times$ over typical high-speed OCT systems, paving the way for densely sampled volumetric data sets and new imaging protocols.