Rabbits are fine, I worked with Dogs, cats & small furries & amphibians all through my pregnancy....
Cats can transmit toxoplasmosis, dogs can transmit toxocara, but only if not up to date with a regular worming programme as its the worms they carry that cause the disease.
You are more likely to contract toxoplasmosis from gardening or eating undercooked meat, which again is pretty rare...
Just normal hygiene procedures such as washing hands thoroughly after contact with any faeces and urine should be more than adequate when handling any animal as you normally would anyway....
I had a blood test early on in my pregnancy as I was a vet nurse & work insisted & I had a high level titre which means I was exposed & now immune to be susceptible to toxoplasmosis...
The midwife should be happy to send you for the same blood test, just say you work with animals
then your mind can be put at rest