It is against the law to travel with children without a car seat and for a good reason to- car crashes are the leading cause of both disability and death for children under 12 years old.
You need a car seat- booster seats do not provide protection in a car crash for a child at that age. I don't know the laws in your state, however, state laws provide children very minimal protection in car crashes. Best practice says that kids stay in a 5 point harness car seat until they are BOTH 4 years old AND 40 lbs. This is a minimum guideline. This is because a child under the age of 4 does not have the bone development to take the force of a 3 point seat belt (lap and shoulder belt).
If an adult were to get into a crash with their seat belt on, they could fracture their collar bone. Can you imagine what this force would do to a child whose bones are not dense like that of an adult?
If a child is under 40 lbs, they may submarine under the lap portion of the seat belt- this means in a crash, they slide under the lap portion of the seat belt. This will severely damage the child's internal organs and their spinal cord.
A booster seat just sits on top of the vehicle seat- it is not attached to the car in any way. A booster seat, "boosts" the child up so that the adult seat belt fits on a child's smaller body. It is so that the lap belt is on the hips (not on the stomach) and that the shoulder portion of the belt lies between the neck and collar bone (backless boosters are made for kids who are at least 7+ and weigh more than 40 lbs). Also, not all boosters do their job, which is correcting belt fit- most boosters do not fit 3 year old bodies well. If the lap belt is on the child's stomach, severe, internal damage to the organs and spine will occur in minor low speed crashes. The lap belt should lie directly parallel to the ground for reference (lie straight across the upper thighs). If you are using a booster seat anways- follow the directions for routing the seat belt carefully) and check belt fit.
Most 4 year olds (even many 5 and 6 year olds) do not have the maturity to sit still. I cannot imagine a 3 year old child has the impulse control to not pick up their toy or play with the seat belt. Would you bet your friend's 3 year old's life based on their ability to sit still? A 5 point harness will keep a 3 year old properly positioned if in the event of a crash (if you can pinch the harness, then the harness it too loose).
There are bigger car seats that fit bigger kids- such as the Evenflo Maestro (50 lb limit with 18 inch top slots for the harness) and the Graco Nautilus (18 inch top slots, but has a 65 lb weight limit).
Statistics show that 95?f child safety seats are used or installed incorrectly. If this was your child, I would highly advise you to get your seat checked by a child passenger safety technician (CPST). You can find one at http://www.seatcheck.org/
and it should be FREE to get your seat checked. Something that may not seem important to you, may be very important in a crash.
For example, when a child is front facing the harness needs to be positioned at or slightly above the shoulders- if the harness was below the shoulders, there would be a TON of pressure put on the child's spine and there would be more head excursion than what the manufacuturer intended. If the child is above the top slots, then the car seat is outgrown by height (which is why I recommend the Graco Nautilus and Evenflo Maestro for their high top slots).
Also, car seat manuals do not stress enough the importance of the use of the top tether in a front facing car seat. Federal standards for head excursion without the top tether is 32" and with it, head excursion is reduced to 28" ALWAYS use the top tether- it is a strap that connects the top half of the car seat to a designated anchor in your vehicle. Cars built after 2002 have top tether anchors in 3 seating positions in a car.
There are 2 ways on installing a car seat- one way is latch and the other way is with the seat belt. NEVER use both methods. You want to get a tight installation as possible. I would start in the center seating position as the center seating position is 43-83?afer than the outboard seating positions in the backseat. You cannot use the latch system in the center seating position unless your vehicle manual says specifically that it can be used. This is because the lower anchors in your car are reinforced on the outboard seating positions with a metal bar going across to each anchor and the center may not have this. A secure installation is when the car seat moves less than one inch side to side and front to back less than 1 inch. Get the car seat in as tight as possible. (test the installation with a firm handshake- you don't need to shake the car seat with all your force, however the tighter the better).