Gathering from the TRs, you and your daughter should not have any problems at all on your way to the summit.
Go at a steady pace.
Depending upon your start time, you may encounter water refreeze at the cable section during the early morning hours. During the afternoon, the ice will be melted by then.
The snow patch near the summit may be a "one-way" meaning only one person can traverse at a time if approaching from opposite directions. Be courteous.
You may be well above the smoke level from the Olancha fire.
Have fun and we look forward to your TR and photos!