I purchased Verdone recently (haven't got around to using it yet!) but the instructions are to keep pets out of the area while it is being applied and until it has dried. After that (according to the instructions), it is safe for pets.
you need a 'semi selective translocated herbicide' and a 'calibrated applicator'. Dilution rate is 1:100. trade names can change but veredone is a watered down/different version of what is available to the trade. NAD are the suppliers of this they are at blakes cross near lusk north dublin. this allows you to spray the whole lawn as the molecular make up does not allow the AI[active ingredient attach] to the thin[ie not broad] leaves of the grass plant.
If you wish to kill any weeds [inc grass] then a non selective translocated herbicide eg round up/ pride is fine.
Ensure you have 3-5 hours of dryness and the chemical [as said by triona] should be good to go after 1 hour as it has then been absorbed into the plant/ grass. This is a rule of thumball the same but as i have mentioned before similar to washing powder if you ate a whole box you might [?!!] feel a bit ill. EU legislation has made it so that chemicals nowadays are relatively safe although guidlines still apply.