I would question most breeders of labradoodles, not many of them are in it for anything other than the money.
Is the breeder aware that you have allergies or a 12 week old baby? As a breeder myself, I would be very, very concerned about this, as although I would always take any puppy back that I bred and the new owners couldn't keep, I would obviously want to do mybest to ensure a permenant home int he first place, and sadly, due to experience I know the chances of that being a home with both a 12 week old baby and allergies are slim.
Labradoodles are not hypoallergenic, no breed is, they can be (not always!) non shedding. That is not the same an hypoallergenic as people are not only allergic to the hair, but also dander and saliva. Also, some puppies in the litter may be non shedding, some not, and if the breeder has told you any different, they are lying. If you really want a non shedding dog, why not go for a Poodle, or Bichon Frise?
I would also want to know about whether the parents were health tested. A lot of 'doodle' breeders will say that the parents don't need health testing as 'cross breeds are healthier', but that is rubbish, and certainly those Labradoodles which have been hip scored show there is no room for complacency. Parents should be both hip scored and eye tested and preferably elbow scored too. If they haven't done this, then walk away, there is no reason not to other than money/greed/not caring about the health of pups they have bred and the breeder saying the parents are 'vet checked' or 'really healthy' is no substitute for proper health testing.
That is just the start. Most people find their first puppies much harder than a baby, even if they feel prepared and think they know what to expect. You need to constantly take a pup out for toileting, give it constant supervision, be able to gradually et it used to being let alone, give lots of short periods of training throughout the day... can you really do all that with a new baby, including having tog et up what could be several times with a pup during the night? Or can you cope with the fact that if you don't you may end up with a pup that is still toileting in the huse at 7/8 months? Can you cope with a pp youhave to have with you, who is undoubtedly (because that is what puppies do!) going to leap all over you and your baby and be nippy, so could bite the baby? You won't be able to just shut the pup out of the room when you need to change nappies etc.
There are very, very few occasions on which I would even consider homing a pup to anyone with a very young baby, for all the reasons above. That's not becuase I'm some horrible cow, but because I know only too well what it is like to have a puppy and how it is likely to turn out.
However,if you do decide to go ahead, please for the sake of the dog and your family, make sure you go to a good breeder.