The Christian Cullen filly was being aimed at the New Zealand Oaks and Harness Jewels after scoring her fourth win at Winton on Sunday, Cox said.
Cox will retain the drive on Goodness Gracious, who would be competitive in the group 1 events, he said.
''With her gate speed she's a chance to run in the money [placings],'' he said.
The Mark Jones-trained filly impressed Cox with her prior run for third in the Southland Oaks in Invercargill.
''She over-raced, which made her run even better than it looked,'' he said.
Goodness Gracious Me would next start at Forbury Park on April 17 in a Sires Stakes series heat, Cox said.
Smiles For Miles overcame tendon injuries to gain her first win for Cox and training partner Amber Hoffman at Winton on Sunday.
Smiles For Miles had the potential for more wins, Cox said.
''She definitely is tough. She jogged it, really [on Sunday],'' he said.
Cox and Hoffman were looking forward to the return to racing of another of Grinfromeartoear's progeny, Smoke N Grin.
The son of 10-win mare Smoke N Mirrors was one of 33 horses in training with the Westwood Beach trainers, Hoffman said.
The gelding raced twice last year for a win and a second placing and was held in high regard by the trainers, she said.
Smoke N Grin races at Forbury Park tomorrow night and Hoffman thought he would improve with more racing.
The stable's 11-win trotter Jaccka Justy returned to racing at Addington on Friday, finishing fourth behind Sol Invictus.
He was being aimed at a free-for-all trot in Rangiora on April 27 but could race before then, Hoffman said.
- Jonny Turner
