Jackie McNamara's side fired blanks at Firhill as they drew 0-0 but showed some encouraging signs in the final third as they pushed for a late winner.
Thistle were foiled by an inspirational Rab Douglas as the Dundee keeper pulled off a number of superb saves, with Doolan also hitting a post late on.
His header against Queen of the South earlier this month is Thistle's last goal after a barren run in the final third that has had them win just one of their last five league and cup fixtures.
The Firhill club's top scorer last season was a second-half sub, alongside Chris Erskine, on Saturday as they replaced Tommy Stewart and Christie Elliot in the Jags attack, and the 25-year-old is pleased to see progress being made in front of goal.
Doolan said: "Rab made a good save for the my first one and then the second one has hit the outside of a post and gone wide.
"On another day, both might have gone in but it wasn't to be.
"The good thing at the weekend was that we were putting balls in the box and when you do that things can happen.
"It doesn't have to be a great cross, it just has to be in the right area and give the strikers the chance.
"We have worked on a lot of things in training and, if we can keep at it, I am sure the goals will come."
Saturday's Firhill stalemate leaves Thistle without a win this year.
They are fourth in the Irn-Bru First Division but missed the chance to gain ground on Barry Smith's third-placed Dark Blues and league leaders Ross County.
Three draws elsewhere in the First Division again highlighted the competitive nature of Scotland's second tier, and while Doolan was pleased with a hard-fought point, the striker has set his sights on a move up the table.
He said: "It was a point gained because Dundee are on a good run but we feel as though we could have won the game.
"On one hand, we were pleased with a point but, on the other, we were thinking, 'we could have stolen all three'.
"We are trying to claw back points on the teams above us and gain points on the teams about us.
"Dundee are a place higher and we have to try and get back as many points as we can and move up the standings."