Diana didn't work hard all the way to her children's births, that's just one of those myths that gets perpetuated. The Court Circular is the official record of all the engagements the royals carry out. So checking the 1981 and early 1982 Court Circular one can see that Diana actually didn't work much more than Kate is currently. Diana married in July, she didn't actually do any engagements until the official trip to Wales Oct 28 to 30th. (Charles meanwhile undertook some official engagements on his own in September.)
She then did intake official engagements in November including the one where photographed she looked asleep. (She was actually looking down in the photo, it's quite a famous one as she's wearing a real 'fairytale princess dress'. Some people interpreted the photo as Diana being bored to tears.)
December she undertook Christmas engagement such as attending carol services. In January she did one engagement (Kate also did one engagement in January) Two in February, then the 16th she and Charles went to Barbados (where the pregnancy photos were taken) until the end of the month.
March she did 5 engagements and then April went on maternity leave.
Diana didn't take on her first official patronage until 1983 (the Junior British Red Cross).
Not a lot of research seems to go on by various people when wanting to be critical of Kate and the amount of engagements she's undertaking. In actual fact it's comparable to Diana's. The then Princess Elizabeth with her first 2 pregnancies did no official engagements, there are no photos of her pregnant. As Queen though with her younger 2 she did.