I don't know if it matters if the toe is open or closed-as long as the sole is flexible enough for her to walk in. We loved and still do love-robeez. My daughter wore those all summer long last summer-we'll probably do the same this year too!
I continue to like a closed toe, like fisherman's sandal - so it's still cool. Open toe I thought made more tripping...and toes open to sidewalk scrapes. etc. Playing in mulch is a huge deal too in open toes...keeps getting in there. Along with any stick treats you might allow that drip...
When she got older, we added an open toe tubber sandal - but it's still not ok for playgrounds.
I went with closed toes because I thought open might be easier to trip (get caught going up steps, for example). In so far as foreign objects getting in, mulch and pebbles, both shoes get them in but it's easier to get out of open toes w/o taking shoe all the way off.
I've also heard to steer clear of the open-toed because new walkers still sometimes drag their toes along the ground and don't have the judgment / self-control to say, "Gee whiz, that hurts my toes in these sandals -- guess I should stop."