jenky thats not the 'sole responsibility' or 'custody' the British embassy is looking for, its nothing to do with the Philippine courts. thou you will need custody of the child.
the sole responsibility the embassy is looking for is who makes the day to day decisions that effect the child's life, who ever ( your mom, aunt, even bio father) looks after the child while your not there, there could be a risk that the embassy could say that person has 'sole responsibility' and not you.
i would always say get a child here asap, the reason being the longer your apart it could be more difficult to prove you have 'sole responsibility' especially if you don't have good evidence and you've not lived with the child for years.But If I understand your post correctly you have already been here for over a year on a spouse visa. So soon that visa must be expiring and then you yourself will be applying for indefinite leave to remain here. Being a settled person here in the UK will strengthen your application to bring your daughter here considerably. So it may be worth considering putting off your application until then.