Got early notice from Tenant - how soon to list

Hi all,

My tenant just gave me notice that they are leaving at the end of the 1 yr lease at the end of Oct. So, I usually put an ad in craigslist and a For Rent sign on the front of the property.

Should I put the For Rent sign up as soon as possible and list on Craigslist ?

Any drawbacks to advertising / listing a bit early ?

Thanks, Richard C