The last paper Twenty Dollar notes were issued for circulation in 1993, the first polymer notes were issued in 1994. Your banknote is possibly a part of one of the several different types of "First and Last" sets issued (not intended for circulation).
The paper note you describe seems to have been issued as a collectors item either as a single paper note or together with the new polymer note, both in a presentation folder. The problem is that neither of them are described as having red serial numbers and the note may also have an inscription on the front.
They are definitely a collectible and, in mint condition and the original packaging, could fetch up to $350 AUD.
I suggest you take your note to a reputable coin dealer who will be able to positively identify it for you and give a more accurate valuation.
Plastic (polymer)
Have another look. The Queen is not on the Australian Ten Dollar note, only the polymer Five Dollar note issued since 1992. Prior to the issue of polymer notes, she appeared on the paper One Dollar note issued from 1966.
The original Australian paper Ten Dollar note (1966 to 1993) was 155 x 76 mm. The trial Australian polymer Bicentennial Ten Dollar note (1988 only) is 155 x 77.5 mm. The new Australian polymer Ten Dollar note (1993 to present) is 137 x 65 mm.
Both old and new Parliament Houses appear on the Australian polymer Five Dollar notes as a symbol of our democratic system of government.
The character on the holographic window of the Australian One Hundred Dollar note is a "Lyre Bird". These are part of the security devices included on all current Australian polymer banknotes.
The Australian Five Dollar note was the first polymer banknote to be released into circulation completely replacing the paper predecessor, and was the first polymer banknote to be successfully integrated into the currency in the world. It also has an impressive list of security features and gadgets to foil counterfeiting.
The new polymer notes are mostly blue but have swirls of yellow and green as well.
The new polymer notes are mostly gold but have a few patches of green and red as well.
The Reserve Bank of Australia advises that the thickness of 1,000 Australian One Hundred Dollar polymer banknotes is 140.8 mm plus or minus 5%. Therefore 100 One Hundred Dollar polymer banknotes would be 14.08 mm plus or minus 5%. The 5% allowance is for wear and tear on circulating banknotes.
The last Australian One Dollar notes were printed in 1982. The Australian One Dollar coin was first issued in 1984. The One Dollar notes were progressively withdrawn from circulation from 1984. They are still considered to be legal tender and will be accepted by banks.
A sailing ship appears on the polymer Australian Twenty Dollar note on the side featuring Mary Reiby. Mary Reiby was transported to Australia as a convict and, after her release, married and became a pioneer business woman.
Australian banknotes are all made of plastic, specifically polymer. Australia was the first country in the world to have all its banknotes made of polymer. The composition of the 5, 10, 20 and 50 cent coins is 25% nickel and 75% copper. The $1 and $2 coins are composed of 92 % copper, 6 % aluminum and 2 % nickel.