Regular No.1 Tabuai-Fidow will miss the Pre-Season Challenge clash against the Warriors at Leichhardt Oval on Friday night with a minor shoulder niggle, and Fuller has been named fullback.
Fuller, who started in the custodian's role for the Indigenous All Stars last week, has played 16 NRL games the past three seasons. He has been outstanding but finding a spot for him in the 17 each week is a tough assignment given the Dolphins' depth in the outside backs.
Tabuai-Fidow has played centre on occasions for the Dolphins, as he has for Queensland, but Woolf said his intention was to play the man known as "Hammer" at fullback against South Sydney on March 8.
"Hammer is our fullback and I have never deviated from that. Hammer will be right for round one," Woolf said.
"If we were playing in a final this week Hammer is playing ... but unfortunately he got a knock on his shoulder.
"It is a big year for him. He is hopefully going to play Origin as a fullback and he is going to play for Samoa at the World Cup.
"I just don't want Hammer having to start the year thinking about niggles. We are giving him a freshen-up at the moment but he will get a couple of weeks of full training from next week and will be ready to go round one."
The new six-man bench in the NRL this year could give Woolf more scope to name Fuller on a regular basis.
"It is something we could look at but I haven't written Trai off in terms of playing somewhere else in the team," Woolf said.
"We have seen in the All Stars and for (the Prime Minister's XIII) last year where he played a bit of wing ... and he played a bit of centre on the weekend.
"He has done some work at centre for us in the pre-season as well. He is going to get a run at centre at some stage tomorrow. It is great to have so many options and so much class."
Woolf is also not settled just yet on where former Brisbane powerhouse Selwyn Cobbo will play in round one. He has been named on the wing, outside star centre Herbie Farnworth, against the Warriors after impressing at centre last week against Gold Coast.
"I'm not settled. He is going to start on the left wing. He's going to play a bit of right centre as well," Woolf said.
"It is a trial so we want to use it to move things around and put people in different positions to figure out what the best combo is for round one. I want to see him move around the field.
"We have five quality outside backs before you factor in (injured) Jack Bostock and that gives us great depth and options.
"I know Selwyn has some X-factor about him. He has a work ethic where he wants to carry the ball. Last year there were games where he carried the ball more than 20 times."