This may be an obvious one but have you thought about investing in one of those air purifiers for her room? The bionic tower one has good reviews. You may also hunt for bedding and furniture without triggers. Some fabrics and pillow stuffers are more tolerable.
I have seen that certain vacuums are asthma certified now. You might want to try one of them. I am going to buy one this weekend. Hopefully that would help.
i am 29 and i have had asthma all my life i found that a lot of household products such as furniture polish, carpet freshner and disenfectants plus a lot of other products made me have breathing problems so try and not use them near your daughter also make sure that you vacuum your daughters mattress regular and turn it over. I also found that i couldnt use fabric conditioner on my bedroom linen, the smell was too strong for me on a night when i was in bed (try this for your daughter) i hope this is helpfull for you please let me know how you get on