Should I purchase Baby Carseat for 6 months baby? [closed]

Its the law in most Australian states, so yes, you should buy one. No discussion required.

Children younger than six months must be secured in a rearward facing restraint

Children aged six months to less than four years must be secured in either a rear or forward facing restraint

Children aged four years to less than seven years must be secured in forward facing child restraint or booster seat

http://www.mynrma.com.au/motoring-services/nsw-child-restraint-laws.htm

When driving with children up to 7 years of age, you must ensure they are restrained in a properly fastened and adjusted Australian Standard (AS) approved child restraint. Driving includes when the vehicle is moving or stationary (for example, when stopped at traffic lights), but not when parked. Only child restraints that carry the AS sticker have been tested and approved as meeting standard AS/NZS 1754.

Child restraints purchased overseas may only be used in Queensland if they comply with AS/NZS 1754.

We recommend you use a child restraint that is less than 10 years old. The restraint will have a sticker showing approval and a date stamp for when the restraint was manufactured.

Don't use a child restraint that has been in a crash. If you use a second hand child restraint, get a copy of the manufacturer's instructions, so you understand how to use it safely.

https://www.qld.gov.au/transport/safety/rules/children/

Children aged under six months must use an approved, properly fastened and adjusted rearward-facing child restraint.

Children aged between six months and four years old must use a properly fastened and adjusted rearward-facing child restraint OR a forward-facing child restraint.

https://www.betterhealth.vic.gov.au/health/healthyliving/child-safety-in-the-car

For an overview of laws around the world regarding babies and infants and car restraints, see the Wikipedia article on the topic (suggested by Dorothy).