How Fast/soon Can I Divorce and Alcoholic?

Ok I am 24 years old and the mother of a 19 month old girl. I have been living w/my parents since a month before my baby was born and have been here ever since. I left my husband because when I was 8months pregnant w/his baby he wanted to break/slam a chair over my belly, so I left him a month before she was born and never got back w/him…..so I have been living with my parents since August of 2007 till present time. I stood by my husband as he was in a rehab center for9month..I did all I could to save our marriage he graduated the program August-2008(the same month my daughter turned #1.) So he went into the program when the baby was 2months and came back out when she was 12months-he got to see her once/twice a month I would go see him whenever I could since I did not have anything(before he went to rehab I was already living w/my parents and meanwhile he was getting drug and using drugs this is how he lost his job of 4years,our 1st home, and our car was repoed thanks to cocaine and alcohol) Anyway when I would make every effort to help him, and he was out in the “real” world for only 3months he was working and living w/his mom (My conditions were for him to save$for us and he had promised me that things would be different that he would be saving to get an apartment and live together as a family should….false promises never happened and last monday he called me telling me that he got fired from the job he had since his boss was nice enough to let him live in the Motel he was working at his boss found him in the room drunk and drugged, he also pawned his wedding ring which I ended up paying for(his and mine-since I was stuck paying all the bills, debts, etc…) Ok so now my question is can I divorce him quick even though we have a daughter? We havent been living together for a while (going on 2years on August) He has spent his time in the same rehab center since 2007. Will it be hard to divorce? Or will it be easy (no hassle) I need advice please I am trying to get away from this man that has done nothing but hurt me both physically/emotionally and never been there for my daughter or myself. His only focus has been alcohol,cocaine, and himself no one else. We got married thru court only November-2006 in Houston Texas-I am providing this info since I dont know if divorce varies from state to state.