It sounds as though you have renters insurance so I would call the insurance company and ask them if they cover damage to the door. I believe they will not - and that the door is covered by the landlord's insurance company. In any event, unless the lease provides otherwise, the landlord should be responsible for paying the cost of replacing the door.
I agree with my colleague. Generally, renter's insurance policies only provide coverage for the contents of the rental property (i.e., your personal belongings). Any damage to the rental property itself would generally be covered by the landlord's policy. Unless there is some provision in the lease stating that the tenant is responsible for such damage, it would usually fall upon the landlord to pay for the repairs.
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As with most landlord tenant matters, you should first review your lease. If the lease is silent on this matter, the damages to the unit should be the responsibility of the landlord. That is assuming the damage was not in someway your fault.
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