Well he clearly acknowledges his fatherhood since he sends child support. I'm surprised its as low as that though. Is that what the Child Support Agency has decided on or is it a private arrangement?
As I mentioned, it depends on whether he was listed on the birth certificate or not. If not, there is a different form to fill out and it may be easier because of that. If he is listed, then yes ideally you need consent from him. If you apply for the passport without his consent, the form will ask you what steps you've taken to try to contact him, and it probably won't look good for you if you haven't made any attempts and may mean the application will be refused.
If you get consent and he signs the form, it should be fairly easy and I don't believe you would have problems going overseas without him being present there with you. It would probably be good to get a written authorisation from him that he consents to you travelling overseas with the child, either in general or for the specific dates and destination that you intend to travel for, just in case anyone questions you at the airport about the consent of the father. Without court orders preventing you from travelling though, I don't know of any reason why you would be prevented once you have a valid passport.
In general, because he is still legally the father (unless he's not on the birth certificate), it's going to be a good idea to stay in contact with him for situations like this. You can reassure him that you don't want to involve him in the child's life but for practical reasons, it is important that you keep each other informed of contact details.
