Hi D. -
Congrats on your new marriage and your little girl. Also, kudos to you and your husband for trying hard to make an environment where at least one of you is home with her. With both of you working full-time and during different shifts, it can't be easy for your bodies, minds, or spirits.
In all your efforts to ensure that your daughter is getting the best possible care, please don't forget to nurture your own relationship with each other because I can assure you that many, many marriages end up dissolving because they fall prey to focusing solely on the child. This straight-edge focus can reduce your energy levels to such a degree that before you know it, you have nothing to offer each other but potentially unfulfilling physical intimacy.
I suggest that you ask your parents to give you and your husband at least two date nights per month to rejuvenate your relationship and rediscover what it is that brought you together in marriage in the first place. If your parents can't help you out, then get a babysitter and/or network on Mamasource to find moms in your area who are willing to watch your child. In lieu of an hourly fee, maybe you could trade babysitting times with other moms who need just as much reconnection in their own marriages as you do (you're certainly not alone...there are many, many moms out there).
My husband and I are about ready to have our third child, and we already have a full house with two young children (our son, who's four and our daughter, who's two). We are definitely anticipating the need for some outside-of-the-home "alone" time, so we've decided that we're going to sign up for salsa lessons when the baby is a few months old because we always enjoyed dancing before our babies came along. Not only is it a unique way to get out of the house and have some fun, it's also a great way to keep in shape and keep our energy levels up for our kids and other late night activities. ;)
The point is, whatever you and your husband decide to do on your own, make the time about reconnecting with each other, not rehashing the day's events...make a rule not to talk about your daughter or fret about work - just focus on each other and don't try so hard to have conversations...just BE with each other.
One last thing, when your daughter is old enough to attend pre-school (say around three), there are city-sponsored programs that are both affordable and very effective in preparing children for the big transition to kindergarten. My son goes to Friendship Camp on Bay-to-Bay in S. Tampa, and he LOVES it. He's only there from 9 a.m. - noon, but it gives him time to get socialized and practice his basic academic skills while giving me some valuable one-on-one time with my daugther.
If you need your daughter to be in a longer-run program, there are tons of private pre-schools that will serve your needs so that maybe you can eventually switch to a shift that's more compatible with your husband's. As your child gets older, it's more important that she get socialized and adjusted to a routine classroom environment than always being with mommy and daddy - just read through some of the other posts on this site, and you'll definitely agree that you don't want to encourage "clinginess."
Blessings to you and yours!