While I understand why Flamed has suggested what they did, it unfortunately is a non starter.
If he doesn't buy anything he'll likely blame OP for it, because she 'ruined' it by asking him to buy stuff in advance. If he does buy gifts, then OP will always feel like he bought them because she forced him to. Neither option make her feel good. I've had this in the past and I felt as shit receiving nothing as I did receiving requested token gifts.
OP, I understand that it is difficult to contemplate leaving when you have a child together, especially. I'd consider couples counselling and if he isn't up for it, then I'd say you have your answer on what you need to do. If he is, give it a go and see how the next 6 months are. If he starts stepping up then play it by ear, but if he doesn't, I'd spend that time getting ready for a split (getting back into employment, looking at places to live, etc), and start proceedings to leave.
It's easy to just tell you to 'LTB' but I think sometimes you need to feel as if you tried everything to be at peace with the decision. Of course, if things ever became dangerous or worse than they currently are, an immediate split would be the safest option for you and your child.
Happy birthday and please, do treat yourself. Order yourself some things online that you'd like and a takeaway for one. Buy in nice chocolates and stuff for the bath. He'll likely throw a strop when your food arrives but he can be swiftly told 'well you didn't want to celebrate my birthday so I'll celebrate it myself'. Take yourself off to the sofa, fire on your favourite film. Let him huff and puff in another room and be on his phone, who cares how he feels. He can do one.