Should we move in together, what do I do?

My long term on/off boyfriend is often unemployed and on welfare past few years with occasional temp jobs her and there. He lives with his parents and he says he pays rent but I don't think he does. His parents have always let him get whatever he wanted up until recently. And they still lend him money. He had his own place once and it was too much for him Financially so he moved back home. He comes over often when he's not busy and stays at my apartment all the time. I am moving very soon to a bigger place and he often mistakenly says " our new place" and he said I can have his tv when I move and says his friend has a table for "us" we can have, and I think he thinks he can move all of his stuff in when I move. We do have a child together and normally I wouldn't mind taking that next step but whenever he has a job it doesn't last and I'm the one paying for food, all of our child's diapers etc. He rarely buys stuff for our daughter and I don't think it's fair. I can't really say anything if he doesn't have a job though.I am constantly running out of groceries when he's around.I tell him that if we ever moved in he would have to helpout with bills and food, and he says he would but I don't know if he would.