New fruit trees - should I allow them to fruit

No.

A young fruit tree - especially a dwarf, or one which has been disturbed by transplanting - doesn't have a strong root system, so there's a good chance that the fruit tree will do one or more of:

1.
Drop all the fruit before it ripens, with the waste of resources that could have gone into building the trees strength.

2.
Produce very small, poor quality fruit.

3.
Lose what little fruit is has to pests or diseses - another waste of a dwarf tree's precious strength.

4.
Have no energy left to grow roots in the autumn (plants love to grow roots in the damp, warm autumn soil) and if allowed to fruit, it gets into a cycle of:
"can't produce good fruit because it doesn't have enough roots, and can't grow roots because it's using all its energy trying to fruit"

5.
Weak young branches will be permanently bent under the weight of fruit (or may break).

.

So unless you have perfect growing conditions or a very strong rootstock, it would be unwise to allow a young tree to fruit - especially bare-root trees whose roots will be suffering transplant shock.

Without a well-established root system, a fruit tree will not perform. The best quality fruit comes from a mature tree which has had a few years to develop a good root system to feed the very-nutrient-hungry fruits.

Thank you for the excellent advice FB!

So if the tree is budding up how do you stop it producing fruit?

Rub the fruit buds off with your finger/thumb, or, I guess if you're not sure which are fruit buds (spur bearing?), then nip the flowers out when they appear, or if they have set fruit take them off

I've planted a couple of apple trees and a pear tree in containers at start of year, wasn't going to let them fruit this year but should I let them fruit next year or would I be better waiting a few years?

Give them the first year to recover from transplant shock. If they are on vigorous roots they may not suffer transplant shock.
See how they grow in the first year. If they manage several new shoots which extend at least 15cm (six inches) then they should be strong enough to bear fruit.
However, the thin spindly branches of young trees (especially dwarfs) are easily bent (and they will stay like it!) if carrying much fruit. So take care not to cause it to have all its branches dragging on the floor.

I've pruned my apple trees to above dog height as one of our dogs would knock the apples off and then play ball with them! She gets shocking flatulence as well ;(

On the plus side though, provided they don't break or get in the way, downward facing branches fruit more