I wouldn't be too worried. I also have a pretty severe dust mite allergy and asthma, but am fine at all of the DLR hotels. Actually, the only time I have ever had problems while traveling with my dust mite allergy is when I stay at my mother in law's home. This is because she is a real pack rat, and the room we stay in has tons of old books, clothes and magazines (not to mention very old shag carpet and curtains). Even when staying there, as long as I don't disturb things too much (like picking up the piles of old clothes, going through the closets, looking in old books)--it is more of annoyace. I double up on my medication there, and bring Benadryl to take at night if I need it. I still tend to cough some and wheeze a bit--but that is to be expected in a house like that.
But in a hotel with very low pile carpet that is kept clean--I am perfectly fine as far as dust mites. Most hotels these days double sheet the bed--putting a sheet over the blankets, trapping any airborne allergens.
I think it is more ideal to have hardwood floors or hard surface floors for living in at your house if you have a dust mite allergy, but for a hotel it is perfectly fine to have a low pile carpet for a short visit at a hotel by a dust mite allergic individual. The most important thing is that the hotel has a basic level of cleanliness. The only time I have been worried about that is in some cheaper places I have stayed over the years (they may not be as concerned with customer satisfaction or are unable to pay their cleaning staff adequately, leading to poor hygene at the hotel).
