Is my husband an alcoholic,bad father, and should I get a divorce?

My husband and I have been married for a little over a year and we have an amazing 15 month old child. We made the decision for me to stay at home with our baby but he never provided any financial support. My father passed away prior to the birth and marriage and left me a small amount of money. This is the money I used to support myself and my daughter for the first year of staying at home. I bought the diapers, the clothes, the toys, books, food, carseat, EVERYTHING! We only use my car to drive our child around because my husband's vehicles although they are new and spendy are impractical (think two seater convertible and lifted trucks). I still owe money on my car and his are paid for all of them. He makes really good money and so did I before I left work. But I have student loans and his dad paid for his school out right. Needless to say my money is gone and I had to beg him to start contributing. I know I could suck it up and go back to work but I hate the idea of daycare. It would be different if we couldn't afford it but we can. My husband maxes out the amount of money he contributes to his 401K (seriously the government won't let him set aside any more) and he has 3 vehicles all his. Money is not a problem even in this economy for him any way. He also drinks a lot. I have never left our child alone with him because he always has a beer in his hand. He still functions and goes to work but every night he drinks; he comes in from the garage after work with a beer in his hand. He drinks to the point where one night he pounced on me in bed (late after midnight) and woke me from a sound sleep then when I didn't immediate respond to fumbling hands and drunk slobbers he walked out and then carried on a mumbling muttered conversation for over an hour. I thought he was on the phone but he was talking to himself. I think that he is an alcoholic but he doesn't think that he has a problem. He did give up drinking for lent and has only “slipped” once to the best of my knowledge. He has left beer bottles on the floor and our child has gotten a hold of one of them pour the beer down her front and all over the floor. I caught her before she drank any but seriously how irresponsible was that of him. My biggest fear is if I divorce him he will get some custody and our child will suffer. He needs to acknowledge his drinking and get help before I feel even remotely comfortable leaving our child with him. Our child is first in my life her needs always come before mine and my husbands. My husband has never gotten up in the middle of the night with our child, never thought hey maybe I should not drink tonight so I can take over bath night. He goes off on the weekends when he wants to do what he wants (hunting, fishing, whatever) I have never been away from our child except when my sister will come over so I can take a break, but this is very rare. I am trying to stick it out until our child is old enough for school and hoping things may get better. My husband gives me enough money to pay my bills and then a $100.00 for groceries, gas, food, clothes every month, needless to say things are tight and I can't afford more than the bare minimum. I am still wearing nursing bras because I can't afford real bras and I stopped breastfeeding months ago. I know that this is only one side of the story and maybe he thinks I am just a bitter stay at home mom. But he never talks to me; we go days without talking. Our 1st wedding anniversary he didn't say a word to me NOTHING. I have tried talking to him and ask him what is wrong but everything is always “perfect”.