It may be possible if the child is a minor and dependent on you wife. Otherwise the child should be making an application from the Philippines.
It is not possible to say for definite because the UK policy states that you "should" apply from your country of residence and if you have permission to stay in a country other than your country of residence as a visitor for 6 months you are not resident. Given your child is only 18 months you would need to state why the child is applying from UAE.
It shouldn't be any more hassle than it would be applying anywhere given that the requirements are the same. The cost should be the same but there maybe local costs involved, I don't know. You will need to check with the British embassy in the Philippines.
Please if you could rate, I would be grateful.
If they are granted a visa to the UK they can travel from the UAE to the UK if the child is on a 1 months visit visa to the UAE.