At the start of the episode we see Doctor Crusher has been in negotiation with the base over the storage and handling of live medical samples.
CRUSHER: Captain. Arkaria Base does not have the medical storage units I have requested. I have seven living tissue samples that won't survive the baryon sweep anymore than you or I would. I've tried to reason with them, but
Since none of the pets on the ship were in areas where the field was supposed to be diverted, we can reasonably assume that they were on the surface when the sweep took place (along with the crew) and were then beamed or shuttled back afterwards.
Since this is a base that is set aside specifically for decontamination of ships in service, one would assume that they have ample facilities to store any pets and plants.
