Fleas?

[Chihuahua_mama]

We just adopted a long-haired Chihuahua, who we named Peanut. We have had her for about 5 hours and discovered a few fleas. We already have a Chihuahua/Pekingese named Princess who doesn't have fleas.

We have already bathed Peanut with Hartz and put a flea collar on Princess, since Princess didn't seem to have any fleas yet. Peanut will get her collar on tomorrow.

My question(s):

Is is possible for Princess to have gotten fleas in a few hours? Will the collar do a sufficient job?

Was the flea bath for Peanut enough? will the collar be enough? Will it benefit everyone to bathe BOTH dogs in a week with the Hartz?

Thanks in advance.