I can't answer for you, but if you feel she is ready for it and the school does then by all means go for it. I have to say that I am not gifted (as far as I can tell) and I started school at 4yo (october birthday as well) and I did well (socially and academically). Like Montana mentioned we live in NY and we have tons of kids start school that don't turn 5 until November. I don't think that's a big issue.
I know how hard it is to let go and them growing up so fast. DS is quite the young man and has never been much of a kid. My DS4 will be 5 next month and he is skipping K and going for first. I know it is a good fit, but I am still somewhat sad about it. I think that is only normal. I would go with your gut about what you think is best and if the school is recommending it they probably know what they are talking about as they don't typically recommend skipping or early entrance unless it is warranted.
About the language, I don't know but I think Spanish would be fun. And I know lots of gifted kids pick up languages easily. DS knows a decent amount of Spanish from life. I minored in Spanish in college so I tell DS words when he asks...and of course he remembers everything so now he speaks spanish, LOL.
