Yes, your Honda will need to be smog checked and registered in California in
order to be legally driven in Los Angeles. If your duaghter was simply
visiting for a short while, no registration or smog check would be needed.
If she was to get pulled over by police for any reason she would simply
state she's on vacation in California and will be returning to Kansas
shortly, however since she will be here for purposes other then vacation,
such as school or employment, California registration will be required;
which will require a smog inspection.
Her Honda however should not have any problem passing California's smog
test, so long as it has been properly maintained and in good running
condition.