Hi @Stilgoingstrong It is not a necessity to have a DBS or be trained in dog first aid to house sit for TrustedHousesitters, but it certainly can be useful, especially for the dog first aid part, especially if there is an emergency situation.
My hubby and I have both a DBS certificate and are trained in Pet First Aid & CPR and sometimes some homeowners may require a DBS due to their particular property which we are more than happy to supply but it is personal preference as to whether or not you have either.
Also as @jcvbva mentioned, there is also the Vet Advice Line available 24/7. 
You may find the attached link helpful.