Possibly stupid question, but please help!

Ab
Can a 9 week old baby already show signs of being allergic to pet dander?
I have 4 dogs & one cat. They are all masters of shedding, I keep my roomba going 4-5 times a day, manually sweep once a day, and swifter once a week. They hang out only in the living room, sectioned part of the kitchen, office, & outside. 
I've noticed that anytime I bring my daughter out of the nursery, or other off limit parts of the house from animals, her eyes turn red, get super watery, she starts sneezing, stuffy nose, and sounds congested. 
When I removed her from the pet areas I always bathe her which seems to help. This seems kind of recent. I only started noticing these symptoms maybe two weeks ago, and it just seems to get progressively worse anytime she's in the vicinity of the animals. Any ideas?