I know of no hatchery where you can order chicks now and have them shipped immediately. The age difference would be too great to brood them with your current batch of chicks regardless and you'd have to split the brooder to have them start integration.
I would wait until the cockerels show themselves so you know what you want for new pullets, then place an order to be shipped to you during temperate weather conditions. Never have chicks shipped during extreme heat or cold. Prepare a grow out pen or isolation area, whatever you want to call it, and move the boys over when they are around 10 weeks old. Before they start terrorizing your pullets. Then work to rehome them. Or keep the best one if you want him.
I have only ever purchased from Meyer Hatchery. Twice. Out of 25 total birds purchased, they goofed up on 1 chick that turned out to be a cockerel. All breeds were correct. I think most breed mix ups occur when a farm store orders in chicks and the employees end up mixing them up in the troughs when they handle them.
You need to have a properly sized coop for all the birds you want. Not a tiny pre-fab. Anything that states the number of birds it can hold is absolutely going to be violently undersized.
You want to have 4 sq ft of floor space and 1 linear foot of roost per bird in the coop along with as close to 1 sq ft of permanently open ventilation per bird as possible with more available to be opened up during warm weather. If you have such a coop, you will hopefully have enough room to create a brooder in the coop using framing and 1/2" hardware cloth. Use a brooder plate or mama heating pad for the heat source. This way the chicks will grow up in full sight of the flock. You can begin integration around 4 weeks of age by opening chick size doors in the brooder so the chicks can come out but the older pullets can't get in the brooder.
When the youngsters are ready, they will roost with the older birds and you can take down the brooder. Usually by 6-10 weeks of age.
As most of their waking hours will be spent out of the coop, your run needs to offer 15 sq ft of space per bird with multiple food and water stations and lots of stuff in the run to engage the flock and keep bored birds from terrorizing the lower ranking individuals.
