Welcome Tia!
Sorry on the loss of your Dobie..... your consideration of a Labradoodle is wise as these dogs are excellent family pets, especially with children!
Yes, there are no guarantee's on the shedding part in the first generation, but further on in the generations it can be a bit more predictable.
The ones with the more poodly coats seem to be a safer bet when considering F1b's. And with non-shed, there is going to be brushwork and grooming involved.
Up side is, when they get wet, they don't tend to smell "doggy" like say a Lab or Dobie.
Find a good breeder you can work with & tell them your family situation....they should be able to watch the puppies as they grow & be able to pick out a pup that will be a good fit for your family.
Also, if they know their dogs, be able to pick out a puppy that is less likely to shed at about 6-7 weeks old.
Best of luck in your decision of your next family member!