Is There a "Super Mario Galaxy DS"? Release Dates for the Galaxy Series

No. There is no "Super Mario Galaxy" game on Nintendo DS. The series exists only on Wii and Switch:

• Super Mario Galaxy — Wii, Nov 1, 2007 (JP) / Nov 12, 2007 (NA)
• Super Mario Galaxy 2 — Wii, May 23, 2010 (JP) / May 23, 2010 (NA)
• Super Mario 3D All-Stars — Switch, Sep 18, 2020 (limited-time digital/physical) — includes optimized Galaxy 1 & 2 ports.
• Super Mario Galaxy (standalone) — Switch eShop (part of 3D All-Stars delisting, not sold separately).

Mario on DS (Contemporaries)

• New Super Mario Bros. (2006) — 2D platformer, huge hit.
• Super Mario 64 DS (2004/2005) — 64 port with extra chars, touch controls.
• Mario Kart DS (2005) — Online via Nintendo WFC (now defunct; fan servers exist).

If you want 3D Mario on handheld, Super Mario 3D Land (3DS) and Super Mario 3D World + Bowser's Fury (Switch) are the closest experiences.