You could, but it won't really work. It's better to get a flea comb and comb out the fleas, then drown them in soapy water. If your cat has fleas, your house is infested too. You'll need to vacuum thoroughly and spray the bag/canister with flea spray, and empty it outside as soon as you're done. Spray every surface in the house with flea spray (the Raid in the purple can seems to work well). Spray carpet, tile, wood, all the furniture, and don't forget drapes/curtains, inside closets, and under beds. Wash everything washable in hot water. 11 weeks is plenty old enough for Frontline Plus. I highly recommend you use this product...available OTC at many pet stores, online, or from your veterinarian. It will kill the adult fleas and eggs as well. Best wishes!