2020 grad here!
You can definitely get by without a car, myself & most of my classmates did. There’s quite a few bus routes that stop right outside of campus, and the DART (light rail) station is within walking distance of campus as well. There’s a student discount on public transit which is cool.
I was able to find housing within walking distance of the vet school, I’d recommend checking out daft.ie to get familiar with accommodations in the area. There’s a few FB groups for advertising housing as well you can join after you’re accepted to UCD.
There’s on campus accommodation as well, didn’t live there myself but many of my classmates did first year.