I've been an API instructor for the last three years. We've had plenty of actually single parents (other parent not in the picture) come through as students. It can be done, but it's a challenge. Your issue is not so much the working day, which is usually 0600-1600 or thereabouts. It's the ass-ton of studying that is required after hours. You're going to be living in your books, both in API and at the VT's. And I do mean living, as in, not much time for the munchkin. Base child care is an option, though it usually has a pretty long wait list, so get on that early.
Who's going to help you with the kiddo in the evenings? And on those days when you've got an 0500 brief? You really don't want to be the VT student who's permanently sniv'ing "no late nights or early mornings...I have a kid". Once in a while is okay, but not as a regular thing. I strongly recc figuring out a full-time child care plan. Mom, mom-in-law, sister, au pair, whatever. Someone's going to have to be live-in help.
Keep in mind, you and husband are both at the beginning of training. You haven't even classed up at OCS. There's no telling what your schedule will be like for the next year. You could get rolled at OCS, he could get held up for something, and it's not like you check out of OCS one day and start API the next. There's usually several months (6+ at present) wait for API class-up. So get a plan in mind, have a backup plan and backups for your backups, but don't feel like you have to get everything set in stone right now. You don't know what your living situation will be like by the time you need it. We have had married couples in the same class.
Re: once you're both winged and in the Fleet. Usually policy for mil-mil couples with kids is for one to be on sea duty and the other on shore, then switch. So you probably won't have to be on sea duty at the same time. That'll hurt careers, as moving up in the Navy means meeting certain career wickets on time, but it can be done.
Co-location is usually workable...usually. As in, they'll work with you, but reality gets in the way. If one of you is flying Prowlers and the other P-3's, they'll try to get the P-3 bubba a Whidbey squadron (though still going to go through the RAG at Jacksonville). If one of you is a Rhino WSO and the other flies P-3's...well, there's not much they can do. There aren't any places that have both. You'll be living apart until shore duty.
Best bet is for you both to be in the same community, though that has its own challenges and opportunities. Mrs Fester also flies E-2's, which meant we were stationed together in Norfolk, but for the first four years we were married, one or both of us was pretty much always gone. That included one year where she deployed, and then my air wing deployed four months later to relieve hers. Our boats passed in the Red Sea, I took a helo over to her boat, we got to spend an hour together, and that was it. I saw her again four months later. We basically time-shared the house. And finding shore duty together when you're in the same community can be tough, too.
There's nothing easy about being a mil-mil couple, though it has its good points. You're going to have to make some hard choices about family vs. career a lot earlier than couples where only one is in the military. I've known many mil-mil couples, and in every single one of them, one or both got out when their minimum time was up. It's workable for a few years, but very difficult for both to make a run at being career officers (shooting for command, etc), and have any semblance of a home life or quality time together. With a kid? Pretty much impossible. Not trying to discourage, just telling you to be realistic about what you're getting into.
Best of luck to you!