Hi Kalbo
I brought my wife and then 9 year old step daughter here in 2009. For my step daughter we had to prove that my wife had sole responsibility for her daughter. For us that took an annullment in the Philippines with a judgement giving my wife sole responsibility for my step daughter. Her real father left the scene soon after she was born. But not before putting his own name on her birth certifiicate and registering a fake marriage to my wife in the NSO in Manila. Me undoing all of that is another story.
Fortunately you have none of those problems and after getting her a Filipino passport, like Graham says providing the father is not going to object/interfere then you should be able to do what you want right now.
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. As your daughter is only five years old now, she will still be young enough to slot into school life in the UK with no problem even if you do decide to wait until you have your own ILR before applying for her to join you here.