Well... one thing that MIGHT help... is that drowning is easy to fix. I've been drowned myself about 5 times for training purposes, not including partial drowning (waterboarding). :P Not fun, but SUPER easy to resuscitate.
Another is to Make Sure she is in the type of class that has a max of 2-3 toddlers per instructor. More than that and the instructor cannot physically keep track/eyes/& hands on all of them. Some of the public pools/Y's have TERRIBLE swimming instructors & policies...(some have great ones, always go view them before putting $ down). Some terrible ones I've seen have toddlers who are expected to hang onto a wall for most of the class (they don't have the arm strength or the patience yet... look for toddler classes that have them on the steps), classes where there are more than 4 (I've seen as many as 8!!!!) even 4 is pushing it) ETC. Another thing to look for are the Mom-n-me classes.
Toddlers should have hands on them 100% of the time, unless they're sitting on the stairs (but if on the stairs the instructor should be facing them at all times and never more than about 6 feet away... aka a 1 second glide&scoop), until they're bobbing/gliding/floating/able to monkey walk the wall/hold their breath on their own and jump up from the bottom, . As they're learning to do these things the instructor should never be more than 6 INCHES away. (Essentially the instructor has their hands right there, but isn't touching.) Kids learning to swim will ALWAYS gulp water (we call it swallowing fishies)... which can be scary (hence the silly name and lots of praise). Learning to sputter though, and to breath selectively is a vital part of the swimming process.
The best classes also have parent seating within about 3-4 feet of the pool stairs, which adds extra eyes and hands in case of emergency. Also siblings/other kids should NOT be allowed to be anywhere near the water's edge during the class. (These are usually the near drowning cases I've personally seen... they're not actually in the class, and they slip in and sink. Parents are gabbing or nowhere to be seen, and the instructors are all eyes and hands on the kids they're responsible for. Do note, I said near drowning... in every single case the sinker has been scooped out within seconds. -Good swimming instructors are hypervigilant and so are parents watching the water instead of socializing. No resuscitation even necessary. ).
The same rules for instructors go for parents as well. Until they're swimming on their own, keep your hands on them or near them at all times (avoid avoid avoid blow up stuff, although tight fitting life vests are fine for non-lesson/non-practice time, you should still stay within a few feet of them), NEVER take your eyes off of them... even when they're capable swimmers, keep an eye on them..
I grew up on the water, later worked in the water, and am essentially half fish. LOVE the water. But fear clouds judgement (hence why drowing was part of my rescue swimmer training). Find a place that you trust, follow a few simple safety rules, and you'll be fine.