Severe as it sounds, your pets, including rabbits and guinea pigs, may have to go. Animal hair, fluff, and fur are some of the leading causes of asthma. At the very least, keep furry pets out of the carpeted areas of the house. Keep your baby's room as dust-free as possible. It's not really the dust itself that's the problem, but dust mites.
Dust mites survive and thrive on minute particles of human skin.
Things you can try to keep the mites at bay include pulling up the carpets and covering hardwood floors with rugs, making sure bedding and pillows are not made from feathers, cleaning frequently to keep dust to a minimum, and washing all bedding frequently in hot water. Put stuffed toys in the washing machine frequently, too. Let your child spend as much time outdoors as possible. As asthma is more common in homes with gas cookers, use a fan when you're cooking with a gas hob. Avoid using your fireplace or wood stove if you have one.