Hi
Dogs are naturally social creatures, living in packs in their natural state. For that reason they are ideally suited to multi-dog households. There are exceptions as with some of the fighting breeds but generally Labradors are well suited to living with other dogs.
However some dogs are a little shy and less extrovert than others. She may just be like that. But it’s very unlikely that this would interfere in the long term with her developing a good relationship with another introduced dog. This is particularly the case with a puppy. Puppies present themselves to adult dogs in a submissive fashion. The pup will not appear to be a threat to your Lab. She will feel confident that her place in the family will remain. Certainly she may initially find the pup’s attention a bit overwhelming.
The most important thing in introducing the pup is to show favouritism to the existing dog. The pup will not see that as being unfair and it won’t cause the pup any harm. Do this until a good bond has developed between the two dogs. So an example of this would be if you were cuddling the puppy and your Lab either appeared upset or even tried to intervene. You should then put the pup down and give her the attention. Similarly always give treats to the adult first.
It is extremely rare for there to be any problems with this sort of introduction. On the contrary I find that a second dog will often resolve a lot of shyness issues.
I hope I’ve been of help and wish you all the best with the new family member.
Kindest regards, XXXXX
Dog Veterinarian
Bachelor of Veterinary Science (University of Melbourne, Australia)