Size of the head has nothing to do with the size of the prey a BP can take down.
Feed a prey slightly smaller to equal your BP's girth size (widest part of your BP's body)
If you want to switch to rats, at first I would recommend feeding something similar to the size of the prey you are already feeding, then after 2 to 3 successful meal upgrade to the appropriate size. (This way it makes the transition a little easier)