Pakistan have been hard pressed to compensate for the missing Ajmal, who has single-handedly won them matches in all three formats of the game in the last five years.
He was reported for a suspect bowling action on Pakistan's August tour of Sri Lanka and was subsequently banned from international cricket after a bio-mechanic analysis found his action illegal.
Skipper Misbah-ul Haq stressed Pakistan must move on.
Pakistan have two left-arm spinners in the squad in Raza Hasan, who took 2-17 in Pakistan's six wicket defeat in the lone Twenty20 in Dubai on Sunday, and the experienced Zulfiqar Babar.
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Pakistan will also miss allrounder Mohammad Hafeez, who injured his hand on Saturday and will miss the limited over series.
But Misbah conceded that Pakistan will have to put runs on the board after being restricted to 96-9 in the Twenty20 match, with Australian spinners Glenn Maxwell (3-13) and Cameron Boyce (2-10) causing trouble.
Pakistan's batting will again be tested after their miserable show on the Sri Lankan tour where they lost the one-day series 2-1 and the Tests 2-0.
Australia also are without their regular captain Michael Clarke who is facing a race against time to get fit from a hamstring injury for the two Tests which follow the one-dayers.