Technically there's no such thing as "hypoallergenic" as you can be allergic to fur or to dander, and all dogs, even hairless ones, will have dander. A lot of poo crosses end up in rescue because their owners were conned into the "hypoallergenic" myth and they were still allergy triggers. Are you allergic or did you just want a low-moulting breed?
Labradoodles are also not small, they can easily grow larger than a regular Labrador and are usually crossed with a Standard Poodle who are large leggy dogs. Poodles in particular are very active and intelligent breeds so you have to be prepared for that. All "doodle" type crosses, if crossed with a low-moult and a regular-coated dog, can just as easily inherit the regular moulting coat, or sometimes grow a thick wiry coat instead. They are often puppy farmed :(
The behaviour things you mentioned such as being able to be left and being good with kids is down to the individual dog and your training. They don't come ready made like that, you have to put in a lot of work initially for that to develop. And even then you could have some incident in the future which means it all goes to pot and you have to pivot your whole lifestyle to accommodate the dog. My little one came to us with separation anxiety, she can't be left at all, she even gets mad if we leave the room without her. Loves people including children, but hates other dogs. She's a Chihuahua cross.
I would recommend doing lots of reading around behaviour, remember a dog with a lot of intelligence is going to need a lot more work than a dog that's biddable instead. For instance, a Collie, that's intelligence, but a Labrador, that's a biddable breed. I saw a litter in rescue which were Collie x Malinois, they are going to be extremely active, extremely intense dogs when they're grown up, I hope that was an accidental litter!
Don't write off something like a retired Greyhound, they do fold up small, but don't all come with perfect behaviour so will need work with house training, training to help them be left, and may well need to be walked on-lead and muzzled out and about as they often have zero recall if they see small furries. BUT they don't need mountains of walks that a more energetic breed like a Spaniel would need.