Yes, I actually wanted to note this too - AOPS's (introduction to ?) 'number theory', 'counting and probability', etc. could be options for your DD (of course, depending on her interest and other considerations) - there is no set 1-straight-line sequence of courses. I've seen more detailed recommendations on possible paths on AOPS somewhere but can not find it right now (though there is always Richard Rusczyk's 'Calculus Trap' short article).
As to the questions of placement ('Am I ready?' and 'Do I need this?'), I find pre- and post- tests (found online) for AOPS books and courses very useful.
Re. 'very driven to practice skills with applications/challenge questions, and not driven by much else, honestly' - yes, the backbone of AOPS *is* a lot of application/challenge problems (as opposed just to regurgitating knowledge/skill) - but probably few, if any, 'real world' problems - say, applications in physics or chemistry.
I think the books are well written. In 'prealgebra', the first chapter is 'arithmetic', and it is started actually from something like 1+1, but then goes on to (the student) proving various arithmetic properties (e. g., distributive laws, etc.), defining division via solution to 'ax=b' and reciprocals, and (the student) proving more arithmetic properties. Of course, some subtle details may be skipped here and there, but compare this to the standard practice in US of introducing proofs for the first time only in a geometry course, which is (normally) taken very late.
BTW, if you find 'gaps', you can fill them going to specific topic in alcumus (it is free), try the problems - the provided solutions would include specific theory/practice references (and possibly video lectures).
