K.L.
I have two girls who are 20 months apart. While I was pregnant, my husband stepped in and did more with my daughter. Up until that point, she was a Mama's Girl, but after a while (it wasn't smooth at first), she would go more places and do more things with Dad. So, when the baby arrived, she actually preferred my husband (he wasn't stuck on the sofa with a nursing baby). However, make sure you take time to spend with your 12 month old while the baby is sleeping or swinging, etc...
One bit of advice a friend gave me was to say out loud "OK, _______, time to swing. Now it's ______'s turn." Obviously it doesn't matter to the baby what you say when you put her down, but it makes the sibling feel like you're asking the baby to wait, just like you ask her to wait.