"The mongoimport tool provides a route to import content from a JSON, CSV, or TSV export created by mongoexport, or potentially, another third-party export tool." Hence i think u cannot use new Date();
in the json file. Try to insert data by using a javascript file.
db.collection.insert({ "counter" : 0, "last_update" : new Date() });
then use command 127.0.0.1/db new.js
Otherwise u should give the datestring in the json to insert docs using mongoimport