Just about any child care center will start an infant sleeping on a cot around 10 months so when they move up to the toddler room they are used to it. That way the transition is much easier, especially at nap time. They should also be making sure the baby is getting to the point of only one nap a day. That is not a valid reason for not wanting a child moved.
Also, you said it is an infant/toddler room. What are the teacher ratios. In Oklahoma a baby room has 1 teacher for 4 infants. In the toddler room it is 1 teacher for 6 toddlers. If a child that is not yet 1 moves up they have to have no more than 2 babies in that group or they are out of teacher/child ratio. I would ask specifically about the ratio and ages of children in the group.
It sounds like they are doing the right thing, especially if they have a lot of calls for infants needing child care. Having a class of mixed babies and toddlers is not a bad idea. This is what they usually call a transition room. It helps the babies get used to sitting in a high chair, feeding themselves, cruising and walking, etc...they should be moved out of this room when they are ready for sitting at a table and doing stuff like easy crafts, painting, coloring, etc...
I cannot imagine why they would not be planning on moving your child to the toddler room anyway at age 1, that throws off their ratios in the baby room. Baby rooms are for 6 weeks up to, at most,1 year old, the toddler room is for kids up to age 2. Then the kids start a regular curriculum based class much like preschool in the 2, 3, and 4 year old classrooms then start Kindergarten.
BTW, your cost should go down since the baby will be classified as a toddler. At the very least on his birthday it should go down quite a bit.