You don't mention whose laws will apply or which courts will decide, so it is impossible to answer the question definitively. But, very few courts anywhere would allow you to recover compensation for the time spent replacing the item in addition to its cost. This is usually not a compensable item of damages.
One notable exception to this rule would be in a probate or trust case where a beneficiary has damaged property and the executor or trustee wants to charge the beneficiary not only for the damage but for the executor or trustees fees charged to estate or trust based upon this incident, in a surcharge against the beneficiary's interest in the estate or trust. In that circumstance, it would usually be allowed, because the executor or trustee is in substance a third-party with respect to the estate or trust.
Similarly, if you had to pay someone to go replace it for it for you (e.g. an automobile broker if the damaged property was a car), the amount you paid to a third-party to replace the damaged property would usually be recoverable.
There is a split of authority between jurisdictions over whether an attorney-party can recover attorneys' fees incurred in connection with an incident like this while representing himself or herself, when attorneys' fees would otherwise have been recoverable in that jurisdiction under the legal theory upon which compensation was sought. Some jurisdictions allow it, some do not, and some do not allow even attorneys' fees from a law firm in which the attorney-party has an ownership interest to be awarded even if attorneys' fees would otherwise have been awardable in the case.
But, a first party's time and effort other than legal work is only very rarely recoverable.
Even if you asked a jury for this item of damages (in jurisdictions like the U.S. and Canada that still have civil jury trials in cases like these), a judge would probably instruct the jury that those damages cannot be awarded.