It sounds to me like you are really doing a great job so far. Being a first time mom is so very hard and there is so much that we fear we are doing wrong. Relax.
I guess the first question I would have is "Why is there such a fear of the dog's bed?" Is it a territory thing? Do you think the dog will nip at her to gain dominance? If so, work on letting the dogs know that in the hierarchy of the family it is you and your partner, then the baby, then the dogs.
Children are natural born explorers. It is not only in their nature, it is how they learn and how they establish feelings of competency and self esteem. If you need to stop her because of allergy issues, then be gentle, she is only doing what her nature is telling her to do. You break that spirit now, and you are on your way to a clingy, fearful baby.
If she really REALLY wants to get in the dog bed, maybe it is because to her it is in her line of view. I would expect that when she is closer to 2 she will want to climb into it because it is more her size, but for now, she is not developed cognitively enough to think in those terms.
If it is "first time mother geebies" (and I have been there too!), then just watch her carefully, but don't stop her. She will go over, crawl on it, roll on it and then head off for more fascinating territory. If it is dog issues, try to keep the dogs in the other room when she is exploring so that they do not feel threatened by her crawling on their beds. If it is allergies, wash the beds more frequently and try to gently redirect her to more fascinating areas. But, again, do not discipline her on this. It is what babies are supposed to do,explore their worlds.
You will do great! And, not only will you sail through this little mommy-moment admiring the adventurer in your little one, you will have the bonus of a wonderful, sharp, and self sufficient little girl, in your life! Good luck!