If your workload isn't very heavy right now, then you should use this time to learn everything that you can. Help out people in higher positions (accountants, your manager, etc.) whenever possible and try to learn about their jobs from doing so. Try to analyze your work and find ways that you can make it more useful, more efficient, more thorough, etc. Use every minute that you're at work to be learning more about the accounting world. I worked for a year in public accounting and learned a lot, but honestly I learned a lot more in my 10 months as an accounting clerk in private accounting, because my job duties initially weren't that demanding so I pitched in wherever possible, optimized my work as much as possible, and because of this, optimizations that I created have been rolled out to the entire team, tools that I created are used by the Board of Directors, and I understand more about the “bigger picture” at my job than many of my coworkers who have been there for 5-10 years.
At some point, I'd like to move in to a position above the clerk-level. However, for now, my opportunities for learning and growth are tremendous because being a clerk has enough flexible time to allow me to be the accounting manager's go-to person. When there's a new project that she needs help with, I'm very frequently the one called on, and this allows me to see things that she's doing as well as the things that I'm doing.
All that being said…
In my experience, public accounting tends to be the area that takes people with zero experience, so if you want to get into public accounting, I'd go ahead and start spreading out resumes right now. Some firms hire in the summer when they've got time to train; some hire right before fall busy season; some wait to hire till Jan or Feb when they're overwhelmed. But, you never know which firm you'll end up in, so might as well start looking now! If you're looking for Big 4, that's a whole different ball game, but for general public accounting, I'd take a vacation day and go to every public accounting firm within commuting distance and hand out a very professional-looking resume and cover letter. And then follow up a couple months later, and make another round of hand-deliveries in a few months. Some people don't think the hand-delivery helps any, but my thought is that it can't hurt, so if it helps in 1 out of 10 deliveries, then that's better than not helping in any!
Whether you have 1 year or 3 years' experience working as an Accounting Assistant probably won't make much difference to a public accounting firm, since the work in private and public is different enough that private experience doesn't count for too much in the public world. Or at least, that's the impression I've gotten. 🙂
Also check into your state's requirements for licensure. If you need to have 1 year of experience working under a CPA to become a CPA, and if you aren't currently under a CPA, then that might be extra motivation to look elsewhere. My state didn't require the work to be under a CPA, which was great, but I know that many do.