Lack of dog owning experience isn't generally a bar to getting a rescue dog. They will, however, want to know that you are realistic about dog ownership and what it entails, and have done your research.
When you say a dog with issues, what do you mean? To be clear, you'll never get a dog that's perfectly formed and perfectly trained with no issues whatsoever - puppies aren't like that and neither are the vast majority of family dogs! Even the two dogs I had growing up, who were pretty bombproof temperamentally - one would snap if you tried to pick her up, the other snapped at bouncy puppies in his twilight years, and both hated cats.
I would encourage you to think about what you would class as an issue that you couldn't cope with. For instance, limited basic training or not being housebroken are both relatively easily resolved. Reactivity towards other dogs or strangers (look out for phrases in profiles like "needs to be walked away from other dogs and people") is far harder to solve (often it's more a case of management) and frankly not for the faint hearted or first time owner.
As a first time dog owner (it turns out having easy dogs as a child teaches you sod all!) who inherited a dog with issues from a friend, I would say it's made me a much better dog owner than I would have been had I got a more "vanilla" dog. He'd already burned his way through 3 owners before he was 18 months old... A crash course in canine behaviour and training if ever there was one, but I'm glad it happened (despite the frequent public embarrassment, expense, occasional tears and a few bite marks on my lower legs!)
With regards to the allergies, I'd expect you to have to go and spend a significant period of time with the dog, and do things that are likely to trigger allergies (for instance, stroking the animal then touching my eyes is how I trigger my cat allergy)
However, speak to the breed rescue! Only they know their own policies. If you're turned down by them, keep an eye out for poodles in general rescues like the RSPCA - they do come up, it's not all mutts, staffies and sighthounds!