Since I am from Dallas, I usually have my own car with me in Austin. So I cannot speak to the cab situation or to any public transit to the Domain area. Someone else is going to have to help you out with that.

Your event appears to be at the Frank Erwin Center which is actually north of downtown, near UT.

You might look at the possibility of getting a rental car. While you would have to pay to park if you went downtown, the self parking at the Westin Domain is plentiful and free. And the Domain is right on Mopac (a toll road) so you can avoid at least some of the Austin traffic if you don't mind paying a toll.

Hope this helps!