I dont think getting multiple males is a big issue. Don't quote me but no I dont believe its ever too late to get shots. I mean I update my dogs every year so. Just take it in to the vet before you bring it home, in case he has anything he coudl pass on to your doodle. I think usually its two females that can fight it out for the alpha position BUT with a good owner, even that shouldnt be too big of a problem. I know plenty of peple with multile males and/or multiple females and a mix of both.
Where si the dog from? If the dog is healthy Id say go for it and just get it its shots asap (for me id want the first round before bringing it home to my other dog? but that may just be me being paranoid). Im not saying not to recuse a dog that may need medical attention. Fantastic if you do... but just make sure you are prepared to give the pup whatever it needs IF it does need medical attention. You have a dog already so you're probably aware enough of the cost