Unfortunately most of the so-called bilingual kindys in HH do not have native English speakers teaching, and sometimes actually quite appalling English is taught. I decided that that was not the support I needed for my daughter's English skills.
However, there is a great kindy at the DESY science plant in Bahrenfeld which is not far from Altona and there is a bus which goes from Altona station, although it's a bit of a walk from there through the DESY site to the actual kindy building. They have a lovely playground, the director is English born and bred and they also have German teachers on site. All the books etc. are in English but all I heard being spoken in the playgound was German so there will also be plenty of opportunity for your child to learn German.
They are a relatively small kindy with the downside that it's very hard to get a place, especially as it's really meant for the on-site DESY families, but they do take a certain quota of "external" children each year. I would contact them as soon as poss. and go and have a look.
http://kinderwelt.desy.de/On the other hand, almost any kindy these days offers "english" classes too, often they need to be paid extra and the quality can vary drastically. Some of them have franchises like Lollipop or Helen Doron sending teachers in, some of them have native speakers offering classes privately etc. There's also plenty of English playgoups etc. that you could join to support your childs English.
Good luck!