hi malena,
i've read a lot of the responses you've gotten, and I have to say i disagree with every single one of them. first of all, yes i'm sorry things didn't work out between you and your ex, but that had nothing to with not being married when you had your child. married couples have just as much a chance of splitting up than non-married ones, and if you had been married the only thing that would have changed would be an expensive and drawn out divorce and division of assets.
second, i disagree with all the comments about the high frequency shuffling being what's best for your child. every kid is different, but i can offer some insight because this is the situation i am currently in: my fiance shares 50-50 custody of his 5 year old daughter, and has since his wife left him when she was 1. they do the splits evenly - every Sunday at 5PM. this gives you an entire week with your child, for the every day work week plus a weekend where it's just the two of you. this is good in a lot of ways: first of all, a week is enough time for the child to become comfortable and established at one house: one bed, one room, etc. - but short enough so that just as the child begins to miss the other parent, it's time to go see them! plus, you get a week's break. i've arranged my work schedule so that on weeks with my SD i work 6 hour days, so i'm home early enough to get her from daycare and make dinner and spend time with her at night, and 10 hour days when she's not with us to make up the time. her dad works early in the morning, and is usually home by 4, so he spends time with her too. im not sure if switching your schedule is possible for you but it's a thought.
finally: i congratulate you on recognizing the importance of having both parents in your daughter's life. unbeknowst to a lot of people, some dads actually DO want to see their kids - for reasons other than they have to pay less money. (who'da thought?!) i will say this though - when it comes time to go to school, the child will need a primary residence, not only because schools refuse to enroll the children without one, but having the stability of one home is less stressful and allows the child to have a home base. at the moment, we're in the midst of a custody battle to determine which school she goes to and who she lives with, and things are looking favorable for my SD to stay with us. mom's don' always win anymore. especially if the dad is in the picture, has remained in his child's life, and continues to provide what's in the child's best interest. dads wanting custody is a common occurrence, and it's NOT about not wanting to pay child support, or trying to screw the mom out of something she wants, or trying to punish the mom or make it so the mom doesn't get something over them - dads love their kids to.
so: good luck, it does get easier, there's the possibility of week on week off schedules with your daughter, and GET SCHOOL PLANS WORKED OUT BEFORE THEY HAPPEN. :) your daughter is very lucky to have two parents who really care about her.