I stand corrected on the attempted murder. However it still doesn’t apply to drunk driving unless someone shows specific intent to cause the wreck in order to injure a specific person.
You are correct; my point being that while most criminal codes may not have a specific charge for "attempted homicide," "attempted assault," etc., there is a general "attempts" charge that can be tacked onto virtually any offense, provided there is, as you pointed out, intent.
Because of the issue you identified regarding intent, the Texas Criminal Code does, interestingly enough, have a specific offense titled, "intoxication manslaughter," which would not apply here because the little girl survived, but it's kind of a specific type of depraved indifference charge specifically for DWI related fatalities.