The Telford MP's private members' bill will be debated in the House of Commons during the 2016/17 Parliamentary session.
The call follows a number of high-profile cases, which includes a 2013 report of a nursery school considering reporting a boy who mispronounced the word "cucumber" as "cooker bomb".
Police were also called last year after a 10-year-old Lancashire schoolboy said he lived in a "terrorist house" rather than a "terraced house", although the county council insisted there were other factors behind the decision.
Ms Allan is calling for an amendment to the 2015 Counter Terrorism and Security Act, which gives public bodies including schools and colleges a legal duty to prevent people from being drawn into terrorism.
Her bill calls for primary schools and early years educational centres to be exempt from this law.
She has been backed by former Liberal Democrat minister Norman Lamb, who has sponsored her bill.
Ms Allan said as a libertarian she felt the present law placed an unnecessary burden on educational, caring and other responsible professionals in carrying out their duties.
Speaking after presenting the bill to Parliament yesterday, she said: "People working with young children have been put in the hard position of having to judge whether a child's actions constitute potential radicalisation or extremism.
"Children's spellings, drawings, or sayings are often influenced by a variety of sources; placing a duty on staff to consider whether these constitute potential extremism damages the relationship between teacher and child. A teacher or carer should not be policing the children in their care.
"In 2013, staff at one nursery in Luton discussed referring a child who drawn a picture of his father chopping a cucumber after hearing the child mispronounce it as 'cooker bomb'."
Her bill was one of 20 which was drawn out at random for discussion during the next Parliamentary year.