On New Year's Eve, I don't want to call my girlfriend.
For what reason would you not call your girlfriend on New Year's Eve?
I don't want to bother her, plus it's when everybody is out partying
If your girlfriend is important to you, it is a good idea to call her or see her on major holidays. If you don't see her in person, you should let her know you care about her and are thinking about her, even if it is a busy day with parties.
I was planning on calling her in the morning.
I get that New Year's Eve is a busy evening for many, but I do think you should reach out to your girlfriend that evening. It's an important night and reaching out to your partner is a good thing to do, as it makes one feel a little bit better about the new year.