Easier Than You Think!
Costumes
Even if you cannot sew, I have used a body suit or plain pajamas or a sweat shirt and pants (In the right climate) and attached a simple set of ears made of felt to a hat or hood, tails made of felt, material or just (safe) fluff ! Then just use kid safe make-up and draw on a face if  needed.
In ANY case ALWAYS be sure the costume is kid safe, fire retardant, climate correct and age appropriate.
Kid Cat made with sweats, fabric paint and felt.
Pumpin Boy made with a SIMPLE sewing pattern from Wal-Mart. This costume is not much more than a bag really!
Fun Foam can be bent glued and cut into all sorts of shapes!
HOME
Who said costumes need to be more than well accessorized clothes? Well Lara Croft here was happy!
BLUE here was a home made costume, sort of fashioned after feetie pajamas! I used Polar Fleece. It handles like felt but is washable and needs no hemming!
Optimus here won second prize at the OTFCC in Chicago in 2003!
And if you don't mind sneezing while you sew......there's always man made fur!
Or.... You find an old dress, add a bit of nip and tuck, a detail or two made with fabric paint and you can have a costume!