We investigate the robust beamforming design for a simultaneous wireless information and power transfer (SWIPT) enabled system, with the cooperative non-orthogonal multiple access (NOMA) protocol applied. A novel cooperative NOMA scheme is proposed, where a strong user with better channel conditions adopts power splitting (PS) scheme and acts as an energy-harvesting relay to forward the decoded signal to the weak user. The presence of channel uncertainties is considered by introducing the outage-based constraints of signal to interference plus noise ratio (SINR). Specifically, it is assumed that only imperfect channel state information (CSI) is known at the base station (BS), due to the reason that the BS is far away from both users and suffers serious feedback delay. Our aim is to maximize the strong user's data rate, by optimally designing the robust transmit beamforming and PS ratio, while guaranteeing the correct decoding of the weak user. The proposed formulation yields to a challenging nonconvex optimization problem. To solve it, we first approximate the probabilistic constraints with the Bernstein-type inequalities, which can then be globally solved by two-dimensional exhaustive search. To further reduce the complexity, an efficient low-complexity algorithm is proposed with the aid of successive convex approximation (SCA). Numerical results show that the proposed algorithm converges quickly, and the proposed SWIPT-enabled robust cooperative NOMA system achieves better performance than existing protocols.