I'm having my hair cut. ( I meant to say this is my decision to ask a barber to cut my hair during this week.
What I understand is you plan for a hair cut in this week. Say it that way only!
I'll have my haircut this week. If you are pretty sure (and confirmed), you may also say...
I'm having my haircut this week. Adding this week would remove an ambiguity and make it clear that you have this plan.
I'm having my hair cut - is a complete sentence and would mean that you are having your haircut now. Something like if someone is asking that what are you doing, you may simply answer I'm having my haircut, talk to you later.