Emmanuel-Thomas, who has already been on loan at Blackpool this season, scored two goals and made another as Rovers destroyed fragile Bristol.
O'Driscoll said: "Jay suits our style of play perfectly and it is quite something for a club like us to attract a player from Arsenal.
"I'm so pleased to have him and hopefully we can help him make progress in his career. He has work to do on his play off the ball, but at this stage he could be anything.
"I'm not sure what position he will eventually occupy as he is not exactly a striker and not exactly a midfield player.
"What I do know is that he fits in perfectly with the players we have and the system we want to play.
"I was delighted with all the team. Bristol had height in the middle with Chris Iwelumo and pace down the flanks so they were always going to be a threat, but we were very brave in the way we defended."
A crazy opening 15 minutes ended with the score 2-2. Emmanuel-Thomas put Doncaster in front from Billy Sharp's pass while some spectators were still taking their seats.
Bradley Orr equalised on nine minutes, shooting home from a left-wing cross by Jamal Campbell-Ryce, but three minutes later Sharp bundled in a cross from James Coppinger to restore Rovers' advantage.
Right back Orr got forward again on 15 minutes and Doncaster failed to spot him stealing in to convert another Campbell-Ryce centre.
But City continued to commit bad errors at the back and on 34 minutes Lewin Nyatanga allowed Sharp to race onto Emmanuel-Thomas' flick-on before firing past Dean Gerken.
Just before the interval came the killer goal as two Bristol defenders collided as they tried to head clear a corner and Emmanuel-Thomas netted his second with a low drive.
When Orr got his third goal of the game on 61 minutes it was into his own net, deflecting a cross from Coppinger to complete a day of misery for Gary Johnson's men.
Johnson said: "We were at sixes and sevens from the start and although we hit back twice, the game was lost in the first 20 minutes.
"We didn't make enough tackles in any area of the pitch and when you fail to do that the opposition are made to look very good.
"I'd like to bring in a loan signing to cover for the injuries we have at the back, but it's easier said than done.
"The players will be working very hard tomorrow and Monday before our midweek trip to Crystal Palace."