Translation:The period goes from October to December.
Period's would normally be assumed to be a possessive form in written English, not a contraction of "period is." "The period's duration is one hour." In spoken English, I have heard something like "The period's too long." but it would be unlikely to be acceptable in written English.
Because dicembre doesn't start with a vowel, so doesn't need 'ad' to sound better and distinguish it from the 'a'. For a more detailed description of this, see http://italian.about.com/od/grammar/a/aa091708a.htm