The goalkeeper is third choice at Anfield but due to suspensions to Pepe Reina and Doni he will almost certainly play against Everton
“We're not here to delve into the players' personal lives, but what's happened to Brad would have tested most people,” the manager told reporters on Friday.
“You can only guess what it must be like to go through what he's been through, but he has done. He's come through it a really strong character."
The Reds face Everton in the FA Cup semifinal but they will without Pepe Reina or second-choice shot-stopper Doni due to suspensions.
Dalglish believes Jones, who has come through a tough time off the pitch after his five-year-old son died of leukemia last November, has the character to succeed in the Merseyside derby.
“We know that to do what he's done has shown a tremendous amount of strength of character.”
Jones had to replace Doni midway through the first half against Blackburn Rovers on Tuesday when the Brazilian was sent off for conceding a penalty.
Dalglish stated: “He will be happy he got a few minutes under his belt at Blackburn and I'm sure he enjoyed his first bit of action, saving a penalty.
“He'll be excited, as everyone else is, about playing. It's credit to Doni that he kept himself fit and active and sharp, and Brad's the same.”
Liverpool’s last appearance at Wembley was in a pulsating League Cup final when they beat Cardiff City on penalties after the scores being level at full-time (1-1) and then after extra-time (2-2).
“The Carling Cup victory was a fantastic day for everyone connected with the club but you get your rewards for what happened on the day and you cannot live in the past,” the former Newcastle United manager said.
“We didn't, we haven't and we won't and we will look forward.
“We've never got ahead of ourselves at any stage and we won't now. Just winning the game will be important for us."