My partner and I are probably in a fairly similar situation - we have just had our first baby after 18 months together. We've had separate finances other then the household bills (which we both contribute to equally, into a joint account) and I pay the mortgage (it's my house, which I had bought before we were together) The difference is that I'm the higher wage earner (2.5x)
When we found out we were expecting our baby, we made a list of things that we would need before the baby arrived, and a month-by-month plan of when we would buy them. We set a budget for what we thought reach item would cost, and took it in turns to get bits and pieces, depending on which we thought we would like to be 'in charge' of looking into (i.e. my DP was happy to research prams/travel systems and find an appropriate one for us/our car/entrance hall. I was happy to pick the cot/bedding. He looked at car seats etc)
I'd say that in the end the split of "who paid for what" roughly reflected our salaries. It wasn't really something that we thought about, but having the list meant that we had a plan and e could both feel involved in choosing/taking responsibility for making decisions (obviously in consultation with each other!)
When budgeting, we put individual expenditures to the back burner when we knew it was going to be an expensive month for purchases. I wouldn't look at shoes (my indulgence!) and he was in the process of getting another large tattoo (sleeve - costing over a thousand pounds) and would avoid scheduling sessiona when money was tight.
If there's no reason to think that you won't be able to afford the baby items, then I think your partner is being a bit unreasonable having a go about how you spend your money - especially when it sounds like you've been really working to Dave and put aside cash. Maybe making a list would put it in perspective and help to prioritise what is really important and when things need to be purchased (i.e. what is essential before baby arrives, and what can wait until after your baby arrives) A list also meant that when friends/family asked if there was something that they could buy for us, we were able to let them know what we were yet to buy.
Good luck with it all - I hope that you manage to have a chat and sort out finances and priorities. It's not feasible to deny yourself everything when finances aren't really a problem. While I think we could all agree that baby comes first, if you have a plan for how you are going to afford all the baby paraphernalia, I can't see why it's impossible to buy anything for yourselves.
PS our little boy is now a month old, we've managed to buy everything we needed (and more, really) Often the stuff that you think you'll need really isn't that necessary! It's far too easy to get sucked in by the hype :-)