Hello there not an expert but I can try:

Ability Score: Unicorsn are strong and wise, you might consider putting the +1 on one of those rather than Dex but as it is is fine.

Unicorns are immune to poison so why do you want another type of immunity? It both fits and is "balanced"

For the spells at will detect good/evil and once per day at lv 3 calm emotions with Cha spellcasting ability seems fine.

And that's it for me. Good luck for this homebrew