NEED a place by March the latest!!

I'm looking for a room for myself and my seven month old daughter. Shes only with me from Sunday/Monday (alternates weekly) until Thursday. She will be with family or in daycare for most of those days while I'm working. I currently live on a Staten Island and am trying to move to Long Island or Queens. It's very important that I have a place by March the absolute latest as I'm being evicted. I'm drama-free, hard working, like to keep things neat and organized and very focused on my own and my daughters future so I don't "party" often. I'd like to live with someone who's open minded about kids and is friendly/social.