We are using Petair too, our dogs had their jabs end of last year then one of them failed the blood test so had to have another shot. Thankfully she passed the 2nd blood test, and we got the results which showed the date of the jabs, their microchip numbers and the blood test result (both results showing a fail then a pass for Laska). We just scanned those documents and sent them to Petair along with all the other paperwork from their checklist and so far so good (we are also paying for the gold service). We wanted them to stay in quarantine for the minimum amount of time, so can't take them with us when we go in 2 weeks (AAAAaaaarrggghhh!!) so they are staying with family until September when we are coming back to the UK for a wedding and will send them then. So hopefully we can coordinate the necessary blood tests etc from Oz then get the other bits done when we are back before they fly. Must say my husband and I are finding the dogs the most stressful bit about moving! Shipping furniture, selling the house and having a 8 month old baby to entertain on the flight doesn't even faze us!!
Hope all goes ok for you.