Hundreds do it every month during the season.
It's not dangerous at all, if you are a competent sailor. Charts and Doyle's Windward Island guide book are all excellent.
Sailing is fantastic around here, especially if you can go south in the NE Trades. Remember though, it is winter here too, at that time of the year, so it does blow during what we call the 'Christmas Winds'.
Plenty of great anchorages; no need to pay for moorings unless you want to go into the 'marine parks'.
This isn't the boonies; food stores are abundant and restaurants that cater to the sailors are in every anchorage including a beach bar-b-q at the Tobago Cays, which is magnificent.
There is an underwater volcano which one must avoid when approaching Grenada, but it hasn't erupted in some years; "feeling lucky, punk"?
I was repeatedly told as I learned my trade on the bay, before sailing under the Golden Gate Bridge to begin my circumnavigation in 1970, "If one can sail the bay, one can sail anywhere." I think they were right, you should do fine.
"Any a**hole can make a boat go; it takes a sailor to stop one"
Spike Africa, aboard the Schooner Wanderer
, Sausalito, Ca. 1964