At Fault Collision: Insurance Q

Had a fenderbender last night, hit car in front. :( This is my 1st at fault collision ever. Deductible is $1000.
http://static.flickr.com/22/91165845_3eb2555991.jpg
Got 2 estimates $1900 and $2800, they involve different level of work.
1) Should I go thru insurance and make claim or pay the whole thing myself ? 2) If go thru insurance should I try to find the best estimate AS IF I'm paying it myself or go for the most complete work (e.g $2800 includes replacing the fender piece & more labor)
Very much a n00b at this... I'm in USA thanks Acura TSX 2004
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<snip>

You're also a n00b at crossposting I see.
I'm outta this one after this reply since you've cunningly posted this identical OT message individually to at least three groups.

Giving your state might help. States have widely varied insurance laws. In some, it's a serious offense not to inform your insurance company. And if the other driver does and you do not, you could be strung up high on suspicion of trying to cover it up by not informing them. That looks pretty bad.
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