I don't know how to tell you to get out of it, unfortunately, this is what life in the Coast Guard is like. Thousands of Coastie families deal with underway situations every day. It is only 6 weeks, have you considered putting your child in daycare, or taking a leave of absence from work? It would cost you a little more money, but in the long run you would still have your job. If you quit your job the time will go by that much slower for you, it is important to stay busy while he is gone. It is a bummer that he will miss her birthday and Easter, can you celebrate those holidays on a different day when he will be home? Make friends with other wives who have husbands on the boat, they will be your best allies and support system while he is gone. They are going through the same feelings and stresses as you. Make sure you explain to your child that daddy will be gone for a while, and make some sort of wall calendar that you can check off together each day with a big red pen, so she can see how soon Daddy will be home. Make it fun for her though, if you are missing him all the time, she will respond to that and behave accordingly.
It sounds like you have been lucky so far to have a land billeted husband, but eventually, everyone has to go on the boat at some point. Make the best of it, and send a camera with him! He will bring back some great pictures! Best of luck to you both.