Does the Nintendo DSi Have a Mii Channel? No—It Has "DSi Face" Instead

No. The Nintendo DSi does not have the Mii Channel. The Mii Channel debuted on Wii (2006) and later appeared on Nintendo 3DS / 2DS / Wii U.

DSi Avatar System: "DSi Face"

• Built into System Settings → Profile.
• Simplified editor: 12 face shapes, 12 hairstyles, 6 colors, 3 eye/mouth sets, glasses/beard toggles.
• Used in: DSi Camera (photo stickers), DSi Sound (visualizer), Flipnote Studio (author icon), WarioWare: Snapped!, Tomodachi Collection (Japan only).
• Not transferable to Wii/3DS. No Mii import/export.

Mii on Nintendo Handhelds

• 3DS / 2DS / New 3DS: Full Mii Maker (StreetPass, QR codes, Wii/ Wii U transfer).
• Switch: Mii creation in System Settings; used in Miitopia, Nintendo Sports, Mario Kart 8 Deluxe (optional).

If you want Mii functionality on a DS-family device, you need a 3DS family system.