"We're going to nominate her to the Fantasy and see what happens," he said.
The Grade 3 Fantasy Stakes is scheduled for May 1 at Oaklawn Park.
Because of the coronavirus outbreak, Oaklawn Park currently allows horses to ship in, but not humans. "If we have to ship her to another trainer, I'd be OK with that," McPeek said, noting that he recently shipped a few horses to Oaklawn under the care of trainer D. Wayne Lukas.
McPeek bought Swiss Skydiver, a daughter of Daredevil, at auction for Peter Callahan for $35,000, and he acknowledged that the purchase now seems like a bargain.
"You never know with any of them because you've got to go through the process," he said. "She's always trained like a really good horse. We've known she's got the talent ... it took some time to bring her around.
"The biggest issue we had was trying to get her to two turns."
Before the Gulfstream Oaks, Swiss Skydiver came in third in her only other two-turn effort, the Rachel Alexandra (G2) at Fair Grounds. The Gulfstream Oaks was the second career win for the filly, who broke her maiden in November at Churchill Downs.
"She's getting the routine now," McPeek said. "I like the fact that she showed speed the last time out. The sky's the limit for her."
Another filly that McPeek has in mind for the Fantasy is Envoutante, a daughter of Uncle Mo who broke her maiden with a 6 1/2-length win Thursday in a 1 1/16-mile race at Gulfstream.
McPeek usually shifts his operation to Keeneland in the spring, but those plans changed after the track canceled its spring meet.
"We had about 50 horses slated to run at Keeneland," he said, adding that he has about 10 horses there now.
"We're kind of soldiering in place between Keeneland and our property in Summerfield," McPeek said, referring to the Summerfield Training Center in Florida.