Take the faucet with you to select a new one. To remove it, turn off the water pump or hose valve supplying the RV. Flush the toilet to relieve the residual pressure and drain the line a little. Unscrew the supply hoses from the valve have a towel ready as a little water may escape. Remove the nuts holding the valve to the sink.
Make sure the spacing between the pipes are the same and try not to get one that would interfere with your cabinetry (similar size base). On my RV, the drain plumbing on the RV is too small to accept tailpipe with the mechanical stopper. Your's may be different.