New Puppy-fleas?

About a week ago i bought home a australian shepherd puppy…
well the problem is, is that awhile ago my moms ragdoll cat got fleas from wondering outside and he brought them into the house and has been there ever since. now my puppy has them and she is only 9 weeks old.
We are moving in about 2 weeks and i dont want ANY fleas getting to the new house.
What can i do with the puppy? Since she is only 9 weeks old i dont know what i can do to kill the fleas before we get to the new house and keep them off.
same with the cat since hes coming too and i think he has some fleas as well.
—And do fleas live in furniture?