So glad I logged on this evening sleepinghunter as we are having the same issue with our DD, who is also 25 months! Been in big bed for about 10 days, in preparation for a holiday where there will be no cots (and we can't take the travel cot). Also she was too long for her cot and waking herself up when she bumped into the bars.
Like your DD, ours is very happy about the whole thing, except for when it gets to morning. For the last 10 days, she's appeared on the landing at anywhere between 5 and 6am. The trouble is, she's really quiet about it, simply sitting down with a couple of books and her teddy, so we aren't exactly sure when she's getting up. But she's so knackered by about 5pm that we reckon it's pretty early.
The problem is that she's also refusing to have an after lunch nap now too. She used to have a good 2 hours, and has gone from that, to absolutely nothing at all. I spent a fruitless 45 mins today putting her back countless times, only to give up and pop her on the sofa with some Cbeebies instead. DH reckons (rightly I think) that because we can't enforce the naptime, she's assuming it's ok to get up when she wants in the morning too. Also, I read somewhere that if children go to bed absolutely exhausted then they tend to fall into a really deep sleep for the first part of the night and early morning waking is almost inevitable.
We have a static stairgate like the one you have, and will definitely give it a go, but it involves having the door fully open, which makes her room even lighter than normal at 5am (despite blackouts).
Both DH and I think it's not a good idea to regress to the cot again. Are you having the same problems with daytime sleeps?