I need some super advice.. help please

Okay this is a long story I'm going to try and shorten it as much as I can so please just bare with me.

My boyfriend and I had a miscarriage last october. A month or 2 later his ex started texting him saying she was pregnant and he is the father we went threw hell for the past 9 months with her changing her story like every other week. Saying it was his and then saying it's her boyfriend baby. Anyway she had the baby and is continuing saying she does not know now who the baby's father is that she sees both of them in him but she named him after her boyfriend. Any way me and her have never spoke and when we have it has never been the nicest of words. Well she has recently been texting me and we have set a day to go get a DNA test kit for my boyfriend and the baby to take and send of ourselfs. Well she asked if would take the baby tomorrow night so she can get some rest and it seemed like he really wanted to so I said that it was fine because if the baby is his I don't want to take this time away from him but I'm just so ify on everything. Is this the right thing to do? Is it to soon? I just need some help...