A couple of questions:
1. When do buyers in your market generally like to view homes?
2. How flexible is your employer with your office hours?
3. Does the brokerage you selected generate leads for its agents, and if so does it generate them for "part-time" agents?
4. Do you have several months of expenses saved up in the bank?
It really does depend on who you decide to hang your license with in the beginning. As others have stated, it's roughly around $1,000 for your local association and MLS dues (it's actually been a little more here in the Baton Rouge, LA area) to begin actively working as Realtor.
One thing to consider is that even if you got several leads right out of the gate, and even if you ended up with pending contracts for all of them immediately, you would likely still be looking at 30-60 days before you realized any payment on those transactions.
Some brokers generate leads for their full-time agents, but don't do so for their part-time agents because they want a certain response time guaranteed, which a part-time agent can't always do. So like @Brandon L. mentioned, at least wait until you are generating (and closing on) enough leads to maintain your current gross income (don't forget about taxes, health insurance, etc.) and also keeping in mind that the winter months will probably see somewhat of a decline in those numbers.
A good broker will help you achieve your goal of shifting to full-time if you show that you are committed to doing so.