Should I quit my shitty job before I've locked in another one?

I work as a night assistant for my University, the job basically entails sitting at a desk from 11pm to 4am 4 nights a week. The management is incompetent and dismal at communicating information, could not even provide me with a uniform shirt in medium size. The late hours really wore me down this semester with not getting enough sleep before class. The job is also not connected at all with my career goals and won't look that good on a resume because it requires no skills. I also think I have a good chance at getting a job with the library that is connected to my future career, but it's not certain that I'll get the job. Also (and I feel a bit immature for feeling like this is a big issue) at the last minute they decided that returners have to go to mid-year training (initially we didn't have to) which falls early morning on the day of and the day after my boyfriend and I's 21st birthday which we've been planning for months and they won't let me skip the training.

I really want to just turn in my 2 weeks notice now, celebrate my birthday in peace, and hope I get the library job but my dad keeps lecturing me on waiting until I've got the new job before quitting the old one and I know he'll be disappointed if I go ahead and quit but I really don't want to have to cancel special plans for a bad job that I don't plan to keep anyway (even if I don't get the library job I'm looking for a different one somewhere else). Should I go ahead and quit?
Added (1). I also live on campus so housing and food are taken care of with or without the job. I'm absolutely going to have to quit it when I move off campus next summer anyway because night assistants have to live on campus.

Read more: Should I quit my shitty job before I've locked in another one?