So, it doesn't seem entirely clear from the Core Rulebook: does one get the favored class bonus (+1 to hp or +1 skill) at first level? I wouldn't have thought so, but I notice that the Hero Lab Pathfinder character building tool interprets the rules so that you DO get the bonus at level one. Is this true?
Under section 4 of the Character Creation Outline it states "...and the choice of gaining a hit point or a skill rank each time a character gains a level (including his first level)..."
So, yes, the favored class bonus does apply at 1st level.
Absolutely, a character gets the bonus at first level if they have chosen their first level's class as their favored class. (And why wouldn't they?)
This is according to Paizo: Favored Classes
You really can't get more authoritative a source than that.
When a player makes a character they choose that character's 'favored class' at first level. Any time they gain a level in that particular class the player can choose to take either +1HP or +1 skill point. I'm not sure why Hero Lab would be calculating it differently.
If your race is Human it may be because Human's get +1 skill point per level regardless.