Absolutely.
Try to find yourself a sitter for the hour or two so you can go by yourself. I KNOW that's hard, trust me. I'm not paying anybody, like there is $$ for that anyway!! I don't trust anyone, and my parent/siblings aren't in the same state to come and watch the boys & I can't overuse my mother-in law. She has a life too.
You might try to explain to her how the library works. (people go there to study, read, it is a quiet place)
She might not get that since she is one. Maybe turn it into a game for her, a quiet one. Let's see how long you can be quiet baby... reward--if you are quiet for the hour mommy wants to be in the library you can pick an extra book for bedtime???? or you have to bring something to occupy her, so she is quiet. (snacks, quiet toy, her own books) You could try to make this trip during her naptime.
It might suck for you, but if she gets loud, you have to leave. See if there is a reading group for younger children offered at the library. She can be in there, you might be able to browse. Even if you're in the group with her, maybe at the least she'll learn she has to be a little quieter in the library, if she is listening to someone read a story & not the one doing the talking.
I went just the other day, my kids are older & like to talk too, but I let them pick out a couple books first, then they sat and looked through them while I found some for myself. I totally get just needing to get out of the house for a minute. whew.
My library is online, I can browse online and reserve books. The librarian will get them and they will be waiting for you for pickup at the desk. If you know what books you want, you may be able to do that, so you can just pop in & pick them up.
But she is just a baby. You need to get out & if you have to take her, what can you do?? The best you can do is find something to occupy her while you are there or make your trip shorter than you would like.