Firstly, got to page 6 before HAVING to chip in!
OP you and your DP are getting so much stick that I'm horrified. It sounds to me as if you have the perfect attitude, the perfect relationship, prretty amazing finances, ideal family relationships and support... what more is there to want?
I think people should back the hell off from questioning your DP. If the two of you are happy then who cares. He sounds great. You both sound great 
And of course famiies can and do work with two working/ career minded parents (and obviously a lot of times it has to), in my opinion I think it is probably far easier if one parent is happy to be at home/ be more flexible with work, whilst the other is more ambitious/ career focussed. It surely saves a lot of aggro and negotiating and of course it doesn't matter what which sex/ gender does which role, so long as everyone is happy.
And self employment can always help boost a CV - even if it is nominal self-employment to cover the years whilst being a SAHP - who is going to check exactly what he was doing or how much - or care?!? It is an excellent smoke screen if it relly worries you. And hey, surely he's a musician? All artists are expected to devote time to their art aren't they? I think his hours low wage are totally irrelevent if you have enough to live on and good budgeting skills as you obviously have OP.
So, I think if you should go for having a baby soon if you heart agrees OP. Don't wait.
Who knows what can come up in the next few years (ill health etc) and whilst you might feel worried about that or have to cope with being short of money, I think neither of you will regret having kids, but if you wait and then can't conceive or something goes wrong, I'm POSITIVE you will look back on this time and wish you had chosen to have a baby now.
Just to clarify my perspective; we decided not to have children straight away, because of wanting to try to buy a house and all the sensible things, but years later with health taking a turn for the worse (pre-exisitng so couldn't get cover) and so-so finances we are still struggling with renting, and now at our age with no great improvement in sight, it is the most devastating thought that now will will never get the chance to be parents
though we would love to adopt but health may rule us out.
In hindsight, we would have managed a baby so much better then than now, but that is something we now have to live with and hope that there is still a chance for us.
Go with your heart OP
x