Right so we'll cut this short:
Many people have different opinions about this subject.
Look at your child and think carefully abt what they are doing and how they are doing it. Is the baby turning it's head on it's own yet? Are they holding their head up on their own? Do they still do the 'wobble' and lose control if you turn them rather suddenly or if they startle? -
If they do not have control of their head at all times then a bike seat with helmet is not an option yet for you.
This leaves you with the option of a car seat secured in a bike trailer, a special baby sling secured in a trailer, or riding with the baby in a carrier of some sort on your person.
You can get trailers second hand for cheap and with some thought and consideration can probably rig up the straps for the car seat. Have a good look at the trailer options you have available to you and the carseat you have at your disposal. If you feel that spending the money on a trailer is too much and you won't use it enough in the future it might still not be the option for you.
The last option of carrier/bike is possible but you must consider the situation which you will be riding your bike. Are you very upright so the head of the baby will still be supported by you chest? or will you be rather sloped meaning support would still be needed for the head? How close are the tubes and handlebars if an accident does occur? Do you feel that the baby and you will be able to safely survive and not be injured if a fall occurs? (will you end up being too nervous to ride in this manner?)
Our children are precious as we all know and we want to do what's best for them as well as make our own lives as easy as possible. Hopefully you can find a good solution or compromise to the problem of getting to the shops easily.