We present an unsourced multiple access (UMAC) scheme tailored to high-mobility wireless channels. The proposed construction is based on orthogonal time frequency space (OTFS) modulation and sparse interleaver division multiple access (IDMA) in the delay-Doppler (DD) domain. The receiver runs a compressive-sensing joint activity-detection and channel estimation process followed by a single-user decoder which harnesses multipath diversity via the maximal-ratio combining (MRC) principle. Numerical results show the potential of DD-based uncoordinated schemes in the presence of double selectivity, while remarking the design tradeoffs and remaining challenges introduced by the proposed design.