Hello, I think that is the case. I'm applying for US MD schools and when I registered, I only saw slots in May, June and July. At the same time, I'm not too familiar with CASPeR website and layout. I know that CASPeR takes 3 weeks to send your test score to the schools and depending on your school's policy, your app may or may not be seen as complete without CASPeR score.
But yes, I suggest registering as soon as you can. Being early doesn't hurt, but being late (especially with rolling admissions) will hurt (unless you have amazing stats, which if you do, koodos to you!)