Muscle memory is key. In order for that to work though you definitely need to TRUST that your hand knows where to go. Try practicing it with your eyes closed. I also have small hands and work with kids who have small hands so I have a little extra insight to this problem. I’ll add a couple of tips that might also help with this:
• Play your white key octaves on the outside of the keys, not on top. My hands are small enough that I will press unwanted keys if I play octaves on top of keys.
Good:
Not Ideal:
• If you are alternating between octaves or jumping to an octave and it is a stretch for you, pivot your wrist so that the middle of your hand stays connected to the keys to give you stability as you swing between thumb and pinky.
• Always center your body in front of middle C, so that your muscle memory is consistent and accurate from where you will ALWAYS sit. If your hand looks unnatural while trying to play, make sure to shift your weight over the corresponding leg so your hand stays in perfect playing position.
• Make sure to also engage large motor skills when you are making big jumps, don’t try to stay glued to the keys. Fine motor skills are not ideal for jumping over large distances.
Good luck!