First of all, don't sell yourself short. $500 of excess cash flow is exceptional when you're a single mom who's still in school! There are a lot of people who are married without children and done with school who don't have that much discretionary money.
Here's what I would recommend in your case:
1) Prepare for the worst case scenario by updating your estate plan. As a single parent, you need to have an estate plan in place if you want to have any say on who your child goes to live with after your passing. Also, if you have life insurance (which I'll get to in a big) you'll want to have some sort of trust in place where there are some guidelines on who manages the money and what it can be spent on. I would have an attorney draft a will, power of attorney, and advanced medical directives for you (this should be in the neighborhood of $500, depending on what part of the country you live in). Also, I would talk to the attorney about whether to create a testamentary trust (which only comes into being when you die) or a revocable living trust (which is set up while you're still alive). The trust will add another $500-1000 to the attorney's bill but will be worth its weight in gold if something were to happen to you. The will spells out who will become guardian of your toddler, while the trust dictates who will be in charge of the money and what parameters you're putting on it's use.
2) Buy a stand alone life insurance policy on yourself. You are young, and I'm going to assume that you're healthy and a non-smoker. There is never a better time to buy life insurance than right now. What I would recommend is buying a policy based on where you see your future going - in other words buy it based it on where you see your earnings, debt obligations, and family situation headed. You'll buy a little more coverage than you need now, but you'll grow into it over the next 5-10 years. I'd rather have you buy a bigger policy now that you don't need to replace than to have to jump through all the hoops again after you earnings go up, you take on a mortgage, etc. I wouldn't take the policy as an employee benefit as it won't follow you as you move from to employer.
3) Set up an emergency fund. This is non-negotiable. The standard recommendation is to keep between 3-6 months of living expenses in the bank, in your case with being a single parent who's going to be going through a job transition, I'd say to go for the longer end of that time horizon.
4) Set up a Roth IRA. In a Roth IRA, you put in after tax money and it grows tax free. You are limited to $5500/year in contributions for 2013 (or whatever your earned income is if it's under $5500) and can take out your contributions at any time for any reasons. If you leave the money in until you're 59 1/2 you can take out both earnings and contributions tax free. Remember that the Roth IRA is analogous to a shopping cart and the individual investments can be compared to a gallon of milk or a loaf of bread. If you want the tax benefits of the Roth but haven't built up your emergency fund, you can invest the Roth in an FDIC insured savings account and tap into it if needed. If you're doing fine with the emergency fund, you can invest in mutual funds which will give you more upside but also come with risk.
5) Hold off on funding your child's education for the time being. You are going through a lot of transitions in the next couple years with finishing school and entering the workforce, after those transitions are done then you can think about putting money away for college as long as you are on track for your retirement.