I think since you all just moved in with each other; he is trying to hide that from his ex- and just look like a dedicated father-figure, that his not wanting you there is not about you or whether he would like you to meet his daughter or not, just that it isn't time for him. I don't think it has anything at all to do with your depression.

I would definitely talk to him though, not right before he sends you off but now, when things are quieter. Are you paying any rent on where you both live or have you in effect moved in with him and are just thinking you have moved in together whereas maybe he's just thinking he has his girlfriend staying with him? Did he move to a different place? Just spending the night with him most nights is not really moving in with him, you have to "share" the place, be there "together" and both have a say and set up housekeeping, etc.

I would talk about the whole relationship and where you and he sees it going, make sure you are on the same page.