Formal:
* Mabilis magalit (literally "quick to anger")
* Madaling mainis (literally "easy to get annoyed")
* Mainit ang ulo (literally "hot head")
Informal:
* Mainitin ang ulo (same as above, but more casual)
* Sungit (means "grouchy" or "crabby")
* Masyadong emosyonal (means "too emotional")
You can also use a phrase like "May maikling pasensya" (literally "has a short patience") to describe someone who is short-tempered.
The best choice will depend on the specific situation and the relationship between the speaker and the listener.