I had just finished law school when I had my first son. I read the book "Parenthood By Proxy: Don't Have Them if You Won't Raise Them" and that really helped me make the decision to be a SAHM. (My husband was very supportive.)
You mentioned that you are studying cosmetology, but you didn't say how close or far you are to completing your education?
A cosmetologist generally earns between $35,000 and $50,000 per year. If you will be placing your daughter in daycare, you should budget between $9,000 and $10,000 per year for child care expenses. (And your daughter will be exposed to many more cold and flu viruses in day care, so she'll get sick a lot more often - which will require you to take more time off of work to care for her.) You will have the added expenses associated with traveling to work: gas, wear and tear on the car, and increased insurance expenses. You will also have to have work attire - which may or may not require dry cleaning. You will almost certainly be buying your lunch on the days you work (which is considerably more expensive than eating at home). Even if you spend just $6 per day - this will be $120 per month or $1440 per year. Plus, it's tough to work up the energy to cook dinner when you've been working all day - so you're more likely to pick up take-out on the way home. This is also more expensive than making a home cooked meal.
If your hubby is worried about the loss of income, perhaps providing him with the cost versus benefit of staying at home or going out and working might make the difference. It is EXPENSIVE to be out there in the workforce. Many people don't realize how expensive this is.
My hubby and I agreed that I would stay home until the kids are in school. Then I'll start working part-time (so I will be home when they get home from school), until he retires in about eight years. Then I will work full time and he'll be the primarily at-home parent. (He calls me his retirement plan!)
Good luck with your decision. If you truly want to be a cosmetologist . . . that career isn't going anywhere. You are more than young enough to stay home for five to ten years and THEN start back with your dream.