Yes, have DD fully
describe what she thinks having a rodent will be like? Does she just think it's going to only be taking the hampster/mouse out of the cage at any time of day and night, petting it as it calmly and quietly stays in her arms or lap, while she coos over it, and that's IT? Does she expect to be able to take it out of the cage and allow it to wander around on its own and not have to watch over it every moment? Has she already had real contact with a hampster/mouse and it was only for a few minutes at a time, so she thinks longer contact will be blissfully like that all the time?
You may need to really explain it to her in a way she gets it, that the rodent will be asleep most of the day. It may be skiddish. It may not like being handled. With your other pets, letting the rodent loose or without minute supervision is not possible.
WHO is going to be cleaning the cage and being responsible for feeding it? Will she
really do it long term? Or will that eventually fall onto you over time once the shine of having a rodent wears off?
A friend's DD had a hampster once. Somehow it got loose. Luckily, the dog did not get it. But, it ended up somehow between the walls between the hall and a bedroom. They drilled a couple holes in the wall to try to get it out. But, every time they would reach for it, or try to give it food by hand, it would scurry the other way.
This went on for a couple DAYS. My friend's husband was adamant, no way were they ripping up the wall to get that thing out. Of course, the DD was upset that it was stuck inside. But, my friend was more concerned about the fact the hampster would eventually die between the walls and not only how upset DD would be about that, and constantly thinking of it still in there. And also about the smell from the decaying animal. Or if it got back out on it's own, the dog might get to it first.
Finally, my friend got the bright idea to go "fishing" for the hampster. It had been days since it had really eaten. (They've still been trying to lure it out by hand.) But, my friend got the bright idea of putting a fishing line around a small hard piece of food. Then my friend sat next to the wall for hours on the third or fourth night, with one end of the fishing line tied around her finger. The other side, tied to the piece of food, was dropped down the hole they had put in the wall to see the hampster. She waited and waited and waited. Finally she felt, at first, a small nibble. Waited, then when she knew the hampster had chomped down on the food, swiftly yanked up on the fishing line and pulled the hamster out. It's mouth was still clamped down on the food.
Needless to say, when that hampster finally died, they never replaced it. The reality of owning an hampster didn't match the dream.