My principal doubt is, if Girona after this international break is gonna still being this good, or they are gonna start to fall behind, maybe they can last until the winter break, and become the winter champions

i remember the alst team becoming winter champion asides of the big threes was Real Sociedad a lot of time ago.
I think some people would have the same doubts as you, including myself. Not to underestimate them, but from our experience in La Liga, that teams that can surprise at the beginning of the season they will not be able to maintain until the end of the season, and that always happens, and maybe we can see from the past few seasons that there are always teams that can provide a surprise but at the end of the season it is still the 3 teams that are in the top 3, Real Madrid, Barcelona and Atletico Madrid. This may also be felt by other teams, one of which is Girona who are now at the top of the table.
Girona's fate is largely determined by three clubs who have had better consistency than them every season in La Liga, Real Madrid, Barcelona and Atletico Madrid. If these three clubs experience a lot of bad days, then Girona can freely lead the top of the standings until the season is halfway through. I'm pretty sure Girona will lose points when facing big clubs, they will face Barcelona in the middle of December.
In other matches, Girona could have achieved maximum results, keeping them at the top of the standings for a while. To become La Liga champions, Girona must have a better mentality, because we know that in the last two decades only Valencia has won the La Liga trophy, to be precise in the 2003-2004 season. the rest were won alternately by the three clubs mentioned above.