The Dervish of Dawn gains the Feat Dervish Dance as a bonus feat at level 1. This feat has the following prerequisites: Weapon Finesse, Perform (dance) 2 ranks, proficient with scimitar. Which I can obviously cannot fulfill on level 1. Can I now us this feat without the prerequisites or do I have to wait till I fulfill them and can use the feat afterwards?
James Jacobs says a bonus feat ignores prerequisites
The bard archetype dervish of dawn (né Inner Sea Magic's dawnflower dervish) does get the feat Dervish Dance at level 1 and can't meet the prerequisites. According to this May 2012 forum post from Paizo creative director James Jacobs, that's okay:
Question: Many classes/archetypes have class features that grant bonus feats. Some say you need to have prerequisites to gain the feat, some say you can ignore any prerequisites for a chosen feat, some just say you gain the feat with no mention of the prerequisites.
Which is the default rule on meeting the prerequisites for any feats gained when there is no specific language in the class feature's description instructing to do otherwise?
Answer: If a class grants you a feat as a bonus feat, you never need the prerequisites unless it says specifically that you do.
Presumably, Jacobs means a lone, named feat, not, like, all feats from a list or something. A fighter, for instance, still must meet prerequisites for fighter bonus feats, but a dervish of dawn needn't meet the prerequisites for the feat Dervish Dance.
By a very strict rules as written reading, no, you cannot benefit from the feat. By any sane interpretation of the rules and with the understanding that writers sometimes make mistakes, yes, you absolutely can.
Ordinarily, situations where you can ignore the prerequisites of a feat in order to use it are called out in the text for the feature, as in this example:
The ranger's expertise manifests in the form of bonus feats at 2nd, 6th, 10th, 14th, and 18th level. He can choose feats from his selected combat style, even if he does not have the normal prerequisites.
We also have a counterexample on the Sorcerer, for the list of bloodline feats says this:
At 7th level, and every six levels thereafter, a sorcerer receives one bonus feat, chosen from a list specific to each bloodline. The sorcerer must meet the prerequisites for these bonus feats.
This would seem to indicate that in either case, whether you must meet the prerequisites or not, the rules should tell you.
The case of the Dervish of Dawn seems like an accidental omission of some important clarifying text from the rules of the Inner Sea campaign setting book to reduce word count than an intentionally vague ruling -- then again, I'm only going off what's on the PFSRD.
The Dervish of Dawn class description and specifically the class feature that grants dervish dance do not contain this text, at least not on the PFSRD.
However, this class feature is central to the archetype, and would render your character almost useless, especially since it would require you to have taken Weapon Finesse at character creation. In this case, we should assume that class features that grant a specific feat do not require you to have met the prerequisites. As this is a feat you are granted at first level and it is central to the class, I would rule you do not need to meet the prerequisites.
As an aside, a very strict reading of the rules would say that you need to meet the prerequisites of the feat since there is nothing specific overriding that general rule. I don't think the rules should always be read so strictly because rules considerations often aren't the only reason words are included or omitted from rules texts.