There is nothing intrinsically "wrong" with the traditional set up you both originally agreed to. As other posters have said, what works for one couple is entirely up to them and considering they both discussed and agreed this arrangement, I think those of you who've had a bit of a go at the OP for feeling worried now her DH has unilaterally changed his mind are being somewhat harsh.
Of course .... things happen, and for whatever reason, DH now feels differently about things, and yes, he's entitled to express this. However .... this time round there appears to be no discussion, he's simply laying down the law about what HE wants to happen, and when OP tries to express her concerns about the new set-up he's suggesting they are airily dismissed with this "as and when" argument. Where's the equality in that ?
I agree a rota perhaps sounds a bit student-house-share-ish, but it's not a wholly bad idea, particularly if someone who's never done anything at home is now cutting back his paid working hours. Apart from anything it's practical - he literally may not realise that certain jobs exist (as others have pointed out) ... but besides that, the point is that if an individual was genuine about sharing out household tasks, would they really mind the idea of a rota that much anyway ? It's a clear way of listing what needs to be done, who's working what hours on what days and dividing up stuff according to necessity, skill, availability etc. The fact he seems so reluctant rings big warning bells for me too ... he doesn't want to commit to anything because I suspect he's already earmarked "his" anticipated free time for other things. I also strongly suspect he's the sort of man who'll argue that when it's on his watch "xyz" won't actually "need" (according to him) doing - which is why it's not been done, nothing to do with his laziness of course ! That's another reason why a rota is a very good starting point for a big life change like this ..... so, right from the start, you can both agree on what needs to be done, and to what standard (e.g. "cleaning" the bath isn't just swishing it out with cold water) so there isn't any resentment on either side about someone not pulling their weight.
However, I'm afraid you're on a hiding to nothing here unless he does agree to a full discussion about the nitty gritty of how a home should be run. His comment about you "not pulling your weight" shows he's either very arrogant, or else he's very ignorant - maybe he's both ? Such a remark implies that he thinks you have the life of riley while he's "slogging his guts out" - and he wants some of that too - and key to all of this is getting him to appreciate just how much you do actually do. I second those who've suggested that you leave him to look after DD for a while but unfortunately, the problem with only doing that for a few days is that he simply won't get a realistic idea about everything as coping for 2 or 3 days with a minimum of housework would be pretty easy. He wouldn't, for example, probably even think about the kind of less frequent jobs you don't do day to day, but still have to be factored in nonetheless such as cleaning windows, mowing the lawn, washing the car, bathing the dog or whatever.
TBH, I think he sounds like something of a spoilt brat stamping his feet and having a tantrum. If he'd not commented about you "not pulling your weight" I'd have more sympathy and understanding for him, but I think he honestly thinks you sit about watching daytime TV and meeting friends for coffee. I agree that part of this may well nbe down to the fact that your subserviant/menial role has caused him to see you in a different light to the way he saw you when you first agreed this. This may well be subconscious rather than deliberate but it could also be a very convenient excuse (insisting you have it easier than him) for him to do even less than he already is. Again, as others have said (I think, have only skimmed), he may well work outside the home 9 to 5 or whatever, but his working day has a very defined start and finish to it where the hours outside of that are his to do as he pleases, whilst being waited upon. Your days aren't like that - and you are also working all weekend. IMO, the existing agreement is already unfairly weighted because he gives no regard to the additional responsibilities you also have Sat and Sun, when he has none.
I think that were you to go ahead and get a PT job, the new setup is likely to end in tears and you will feel terribly resentful, a lot more tired, taken for granted even more and wondering why on earth he somehow has more entitlement than you do to R&R. The only way any sort of arrangement works is when all parties feel reasonably content with their lot with a fair division of labour and responsibility. Okay, for lots of us life is crap, no getting away from that, and I'd say that only the fortunate few have jobs they truly enjoy .... but sometimes you literally don't have any choice and just have to get on with it. What would make you particularly unhappy though is feeling that once you get home from the crappy job, your partner takes the piss by leaving all the housework/childcare to you - and that's what I fear will happen here unless you genuinely trust him to pull his weight.
He has got to talk to you or else I'd refuse to do anything to change the status quo until he does. This is supposed to be a partnership, not a dictatorship. I'd start by asking him to explain WHY he thinks I'm not pulling my weight. If it really needs spelling out to him I'd even go so far as to keep a diary detailing what time I got up (and what time he got up), how long this took me, how long that took me etc., add it all up (do the same for the hours he worked), tot up how long I spent watching TV/reading a book/surfing the net etc (do the same for him) .... you get the picture. I wouldn't like to do this - you should be able to trust that he'd take you at your word and appreciate the fact he has clean, ironed clothes, home cooked meals, clean and tidy rooms etc .... but if he refuses to accept you work hard this might be one way to ram it home to him by showing him in black and white.
I almost wonder you know if someone else has been bending his ear about this (workmates, mother in law, friends) ? It's funny how the arrangement worked well but now it's all about turn and he's refusing to discuss alternative solutions properly, instead of making demands. Makes me think that perhaps someone else has planted a seed about him being used or some such similar nonsense ?