I am claiming compensation for property damage due to negligence.
I will simply using the money to replace the damaged items.
Can I also claim for my reasonable time in replacing the items? For example, one hour per item to travel to the appropriate shop, find a suitable replacement, buy it and take it home.
If so, at what rate should I charge for my time? Would my hourly salary rate be appropriate?
You certainly can claim whatever you want. Will you be granted it though?
Time is money indeed, and replacing the damaged items requires some time not just items themselves. The question is how much time and at what rate?
Your duty will be to mitigate the damages and so to minimise the time and its cost. Will your normal hourly rate be applicable? Only if you have to use your actual work time and miss out on earning for those hours. It will probably be unreasonable to use work time in the first place, let alone that you may not necessarily miss out any earnings in case it's a salaried job and your boss is fine to just let you go for a few hours to sort out personal issues.
If the time you use for replacement is evenings/weekends then you would need to quantify how much you miss out on not doing what you would do otherwise.
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.
