The readings are fine De.
13.7 is good with engine running and the 12.37 is over 12 volts but not quite 13. That could be because the battery is not filly charged yet... I would hook a battery charger up to it when itgets home and let it charge for for a few hours, remove the charging cables and then putthe volt meter on the battery and see what it says...
Otherwise if she is going to be driving for awhile coming home that may well work pretty good for charging it up as well..