Sleep training at 13 months

Hi! We co-sleep with our baby since he was born. But we are ready to sleep train him. He doesn't drink milk during the night. His schedule is dinner, bath and milk before bed, which is 7 pm. He wakes up now and then but as long as I'm next to him he goes back to sleep and sleeps until 7 am. He also just started going to daycare few hours a day. We pick him up before his nap. He cries in the daycare and still getting used to it. We will send him full time soon. I'm wondering if I should wait to sleep train until he is used to daycare or I can do both at the same time. Problem to co-sleep is my neck is hurting and weak every morning as he literally sleeps on my shoulder sometime during the night. And we sleep that way until the morning. Please help!!