'if your DP can't even manage to look after his DD for 2 weekends a month without prioritising his hobby over her then I doubt he will be given custody. If he did it would be a travesty. You are young with no children so i will tell you it is not OK or normal for a parent to leave a small child full time for work then for a demanding hobby 4 or 5 nights a week and for weekends. The clue is in the word parenting; you parent them. but your DP sounds like a selfish bastard bith towards you and his DD. Does he just want to punish his Ex or actually bring up his DD?'
The above, exactly. This is totally, totally wrong. I cannot believe that your 'D'P put you on the court documents, either with or without your consent, frankly - good god, he has known you for six months and he's putting you forward as a legal guardian for his child? Even if you agreed, that in itself shows a serious flaw in his parenting skills. To be blunt, your relationship is a fairly new one, no offence but it's not a given that you will be together in a year.
I'm not saying that he feels any need to punish his ex in any way, but it DOES sound as if he's seen the option of having his DD here, facilitated by YOU, and is jumping for it without, sadly, the slightest regard for his DD's actual wellbeing. Or yours. Or that of your relationship.
For his DD to be ordered to stay here, to be looked after mainly by a woman she hardly knows and who's been her dad's partner for only a short while, instead of living with her mum and sister, is not at all in her best interests. If her dad were to radically overhaul his working patterns and give up his hobby to accommodate the huge change, yes it would be less traumatic for her. But it doesn't sound as if he will.
As said above, him putting your name on the documents without having DAYS, WEEKS of heartfelt discussion with you on how you would both feel about it, is a massive, massive red flag. It shows more than anything else how he is thinking mainly of himself here. That he has little to no conception of how massive an upheaval a change in custody would be for his DD. He is on course to create one almighty mess if - heaven forbid - he gets his way.
You would very much be caught up in that mess. It is clear that your DP is acting extremely selfishly, thoughtlessly, and that doesn't bode well for your relationship anyway. I urge you to make it very clear to him that, six months in, you will NOT be a stepmother. That he WILL be taking sole responsibility for a very fragile child, should he get his way. That if he has any vision of the future which features him being able to continue as now with his hobby and working patterns, he needs an urgent rethink or to withdraw his application.
I really, really feel for his DD. If you have any fellow feeling for her, please don't feel that you can't rock the boat - rock it NOW, before it capsizes completely a couple of months after the poor little thing comes to live with you. Good luck.