The six-year-old won at the highest level in last year's Group 1 Kingsford-Smith Cup and almost died following complications from surgery to mend a leg injury after being galloped on in the Stradbroke.
It was the second serious injury Vega One has suffered during his career after a suspensory injury almost ended his career in the Stradbroke Handicap the previous year.
"I almost thought he was going to die after he got an infection after last year's Stradbroke," Gollan said.
"But, he's back now and is coming along well.
"He missed a jump out on Tuesday, which is not ideal, but I worked him instead and his recovery was very good."
Gollan has booked Ben Thompson to ride Vega One while Ryan Maloney will partner Baller.
Vega One will have his next start in the Group 1 Doomben 10,000 over 1200 metres on May 14 with a Stradbroke Handicap start for this year still undecided.
Baller also is making his return to racing after a summer campaign which included three placings at Listed and Group level before a last start tenth to Isotope in the Magic Millions Sprint at the Gold Coast in January.
"Baller trialled well behind Rothfire at Doomben recently and I worked him alongside Vega One on Tuesday and his recovery was also very good," Gollan said.
"I'm not sure if he'll run next in the Doomben 10,000 or he could wait a month and go in the Kingsford-Smith.
"Of the two, I probably have to favour Baller this week.
"I think realistically the Kingsford-Smith Cup is Vega One's go and I'll see how he's going then whether he pushes on to the Stradbroke.
"If he does, I'm hoping it's third time lucky for Vega One."