Unfortunately no, it doesn't exist.
Laying year round eggs is pretty much the bastion of commercial hybrid layers, and even then they tend to go off lay over winter if they're mature when winter comes around.
Leghorns and utility australorps lay better than most birds, but are not usually considered dual purpose.
With some of the lighter breeds, as long as you breed pullets to start laying at Easter, you should get a share of winter eggs... But it's not guaranteed.
Let's try to put it in terms of what's possible:
1. autosexing... Firstly, is that necessary if you're breeding partly for meat? The cockerels will show their true colours in time to be table birds... The pullets will lay. But if you really want autosexing in a single breed then you're after faverolles (which can be sexed fairly young, though not day old), legbars, rhodebars, or maybe pile leghorns, something like that... Incidentally once you get to know your breed most people can sex them at a few weeks of age pretty reliably... For instance new hampshires, which mature early, are pretty easy to sex at 3 weeks. But it takes time to become familiar with your breed.
2. Low broodiness (feeds into laying ability: broody birds never lay as well as non broody ones). Light sussex are the obvious dual purpose choice, but they go broody at the drop of a hat. Barnevelders are not very broody prone (but I've never met a barnie that lays as well as I'd like... Though they're no worse than other show bred birds like the big glossy australorps). Faverolles are reputedly not too broody prone (but will sit). New Hampshires aren't broody prone until their second year. Most of the heavy breeds like brahma, orpington, cochin, indian game and other game birds are very broody prone and therefore don't lay many eggs when you do the count.
3. Early maturity. This helps with sexing (by comb) as well as table use (not too tough/old to eat when finally table size) and laying ability (they come into lay earlier) etc. Mid sized birds like New Hampshire or Australian langshan are fairly early maturing, with langshans a bit later than New Hamps. Langshans aren't too broody prone but perhaps a bit more so than New Hamps.
4. Winter lay. Few purebreds bother, but the layer types like leghorns come close... Barnies are supposed to be decent winter layers as are brahmas (but the overall egg count with both breeds, in my experience, is low). Australorps, if you get the utility layer version, lay well in their pullet year, often laying through winter, but as I said they're not table birds. Show australorps don't lay particularly well (compared to utility ones) and mature late, so I wouldn't peg them as table birds either... Many will claim differently, but make sure they're actually eating their birds and counting eggs... A lot of people have inflated ideas about australorps. (Sorry any australorp lovers... That's just my view.)
5. Moult. Moulting speed (faster = better) has generally been a guide to high egg laying ability, because faster moulters come back on the lay more quickly. Commercial hybrids are brilliant at this, but it's much rarer in purebreds generally.
My vote... Australian langshans (which because of their smallish size mature early, and lay quite well, yet have better table weights than most layers)... Or make your own cross out of leghorns and something heavier like a game bird (as I'm doing as we speak).
I bet I've offended every other byp member, but I mean well...
