Carrots can be grown most of the year.

They like a good friable soil at least 300mm deep, sow seeds after an above the ground crop such as tomatoes or cabbages.
Sow seeds directly in the soil in rows twice the depth of the seed. Keep moist; don't let them dry out, especially in the summer.
A good idea is to cover the rows with wet newspaper for three to five days to allow the seeds to strike. Don't leave the paper there for too long as the seedlings will go lanky. Seedlings usually pop up in seven to ten days.
When the carrots starts to form, around four to six weeks they will need to be thinned out. The carrots you pull out, you can either have a go at transplanting them into another row, which is not always 100% successful or used them in a stirfry The chooks would probably like them also.
Green Carrots you will need to hill up around your carrots with soil, if they are protruding out of the ground as they will eventually go green, green carrots will make you sick as with green potatoes.
There's nothing better than going out in the garden and pulling the biggest and the best carrot you have, especially in front of a friend or two.
Carrots dislike fresh manure, liquid fertilizers and compost as these will cause them to fork or go hairy; they will also grow more tops than actual carrot. They also don't like being grown with parsnips.

Beetroot best time sow March - November

They like well decomposed manure and compost and a good feed of liquid fertilizer once a fortnight after bulbing.
There is no need to hill up beetroot with soil or compost, as you do with carrots as they grow more on top of the soil than under the soil, and hilling up could cause deformity.
Sow seeds directly in the soil in rows 300mm apart and 15- 25mm deep. Keep moist, again don't let them dry out, some avid gardeners prefer to soak their seeds over night, which helps to ensure a better strike. I also soak my Corn seed overnight.
Thinning-out - beetroot also need to be thinned out to at least 50mm apart to allow the beetroot bulb to form, as with carrots you can also have a go at transplanting the pulled seedlings, you only need to cover the roots don't bury the whole seedlings.
The main pest of beetroot is the Beet webworm and the minor pest are the Carrot aphid, Cutworms, Fennel aphid and the Vegetable weevil
It has been suggested that you can achieve a good healthy crop of beetroot by giving them one good feed of Boron when they are about six weeks old.
Beetroot has a special importance in overcoming cancer, you can find more information on a web site by Walter Last www.mrbean.net.au/~wlast
A good Variety of beetroot to grow is Early Wonder
Storing Beetroot the best way to store beetroot is pickling and making Chutney. Here's how I go about it.
First of all you need to cook the beetroot.
Chop of the tops (you can also eat the leaves, cook in a stirfry) of the beetroot wash, then boil until the beetroot is soft. Strain, then peel the beetroot and let it cool.
Pickling:-

1. 2.2 litres of white vinegar
2. 25grams of salt
3. 1-1/4 cups of sugar
4. and any pepper, cloves or spices to suit your own taste

Boil all ingredients for 15minutes. Let cool, strain, and poor over the pre-cooked beetroot in sterilised jars

1. 1kg of pre-cooked Beetroot chopped
2. 500grams of onions chopped
3. 2 cups of sugar
4. 1 tablespoon of salt
5. You could also add an apple and a hand full of sultanas.

Just cover with vinegar, boil all together for 25 minutes, then thicken with one or two tablespoons of flour mixed to a smooth paste and boil for another 5 minutes, store in sterilize jars when cool.

Good Varieties of carrots to grow in good soil are All Seasons and Top weight. Where the soil is not so deep you could grow a shorter variety such as Redland or Royal Chantenay from Eden Seeds.
The main pest of the carrot is the Carrot aphid, Cutworms, Fennel aphid and the Vegetable weevil, for a deterrent just give them a strong hosing.
Saving and collecting Carrot Seed you can save carrots seed if you have planted out a non-hybrid variety, just let your biggest and best carrot keep on growing, avoid over-watering or it will go eventually go rotten. Seeds are produced in large flower heads and will grow over a metre high. As the flower heads dries out, cover the flower with a paper bag. When the flower is totally dried out cut the stalks off the carrot, gently shake the seeds off the stalk and store in a cool place such as the bottom of the fridge, now you have carrot seed for your next crop.
Best place to store your carrots, is just leave them in the ground where they are growing as organic or home grown carrots don't seen to keep all that well. Carrots do loose most of their goodness after a matter of hours, so fresh is best.
Sow carrots two or three times a year for continual supply.

Don't buy carrots in punnets, waste of time

Parsnips prefer cooler weather - best times March-September. Their growing conditions are similar to carrots. I have problems growing good parsnips on the south east coast.
A good Variety to grow is Hollow Crown.

Turnips best time sow March - November growing conditions are similar to beetroot.
They like a feed of liquid fertilizer once a fortnight after bulbing.
You can also eat the leaves, cook same as cabbage.
A good Variety to grow is Purple Top White Globe.

Radish can be grown most of the year they like well composted soil, lots of water as they are quick growing, sow seed directly in the soil in rows twice the depth of the seed, seedlings take three to seven days to pop out of the ground. For a continuous supply sow seeds once a fortnight. Great for salads.
A good Variety to grow is French Breakfast.