Confined to barracks under Covid-19 restrictions like the rest of New Zealand, Baker watched his latest Tulloch Stakes winner from the confines of his Cambridge lounge, with the son of So You Think saddled by Stephen McLean, foreman for his son Bjorn.
"He won well I thought," Baker said. "He went to the line well and he is improving.
"He was beaten by two top-class fillies last start in Funstar and Probabeel.
"He will back up into the Derby (Gr.1, 2400m) next week. You always wonder if they can run the 2400m and not many horses can, but he will have his chance and he plugs on well."
Quick Thinker is raced by OTI Racing, who have enjoyed good success with Baker and his training partner Andrew Forsman.
While Baker believes Quick Thinker will perform well at Randwick next week, particularly if there is give in the ground, he acknowledges the horse has an affinity with Rosehill.
"He certainly likes Rosehill," he said. "He won the Ming Dynasty (Gr.3, 1400m) there in the spring and was good in the Phar Lap Stakes (Gr.2, 1500m) last start. He doesn't seem to mind a drop of rain and Randwick can get pretty wet.
"He has just kept progressing. He took a bit of getting fit this autumn, being a three-year-old colt."
Baker gave credit to travelling foreperson Aliesha Legg, who returned to New Zealand earlier this week when New Zealand announced it was going into lockdown.
"Aliesha has done a great job with this horse. We got him swimming as well, just to try and get him a bit fitter and he was a little bit behind the eight ball.
"Unfortunately, she had to come home on Wednesday for the lockdown, so Bjorn's staff took him over, but she did all the work and got him a bit fitter.
"I spoke to Stephen McLean who is Bjorn's foreman and he said the horse has pulled up in terrific order."
Baker had previously won the Tulloch Stakes with Our Palliser (1987), The Bill (1993), Harris Tweed (2009) and Jon Snow (2017), while Madison County finished runner-up in the race last year behind Angel Of Truth, with that pair filling the same positions in the Australian Derby a week later.
"I think it is a good lead into the Derby. We ran second last year and the same horses ran the quinella the following week.
"Jon Snow went on to win the Derby, but some of my other Australian Derby winners didn't run in the Tulloch," Baker said, referring to Mongolian Khan, It's A Dundeel and Nom du Jeu.
Should Quick Thinker win next week's Australian Derby, it wouldn't be OTI Racing's first Classic success with the Baker-Forsman team.
"We have been rather fortunate that we had a New Zealand Derby winner for them in Vin De Dance, who ran fourth in the Australian Derby, plus this guy and we've also got a mare for them called Vee Cece and we think she is stakes class," Baker said.
James McDonald, who rode the Baker-trained It's A Dundeel to win the 2013 Derby, rode Quick Thinker on Saturday but has committed to Castelvecchio in the Derby.
"I would love to keep McDonald because he rode Dundeel, but he is riding Castelvecchio," Baker said.
"There will be someone looking for a good ride like my bloke."
There is a pool of 25 jockeys who can ride in Sydney after the state was divided into regions to help minimise contact among riders.
While he will not be on Quick Thinker, McDonald believes he is a genuine Derby contender after the $2.70 favourite beat Zebrowski ($4) by 1-1/4 lengths with Diasonic ($13) another three-quarters of a length third."He is a proven wet tracker. He is fit and he'll be a force to be reckoned with come the Derby," he said.