Not only will alkalines corrode and ruin your gear, they are also considerably more expensive than NiMH batteries which can be recharged something like 500 times. Just do the math....

Alkaline batteries don't typically corrode when they're sitting there in the package, unused. That's why all the packages you buy have long expiration dates on them, like ten years in the future. But once you start using them, even a little bit, then watch out. The worst thing you can do is partially use an alkaline battery then leave it sit in your device. Almost guaranteed to corrode in that case.

What I should have done was check her once a month by activating her singing mode?

you must visually check the batteries themselves for signs of leakage.

knives, for instance - they at least don't use batteries....