The first egg from one of our Hamburg pullets was laid when she was 26 weeks old and the others followed within a week or so for the most part. The last girl laid her first egg at 29 weeks. So, it seems like your girl is right on schedule!I was really excited to learn that they're such good layers but my girl is now 25 weeks old and NOT ONE SINGLE EGG from her. I do let them free-range (although I've caught them twice now in my closest neighbors' yard. I immediately herd them home and close them back into the run. My neighbors don't seem to mind but I worry like crazy about pesticides and everyone around me seems to love them along with weed killers. UGH. Anyway, I've scoured the tree lines and gardens and shrubs and haven't found any hidden nesting areas. Finding alternative, more natural places to lay was one thing I read about them...which I do find endearing that they are still wild enough to prefer but not convenient for we caretakers. What's the average age your pullets start laying?
I used to raise ducks in addition to chickens and I love how chivalrous the male birds are of all types can be. Each drake had his mate and they would team up when keeping watch...one would take the first shift while the other grazed with the girls and then they'd switch. It was a beautiful sight. My first rooster was very quiet and respectful of all creatures but he died fighting for his ladies.We were all heartbroken when we lost him. I don't mind the stand-offish personalities of the Hamburgs...It makes for much harder targets to predators than so many other breeds. It's no surprise that they get loud when laying...from what I understand, their eggs can be quite large in relation to their size. I don't envy them!!
I'm not in town either but also not currently set up for an additional breeding flock. I had only two hens for about a year and a half before I finally upgraded coops and added 5 more to the flock, one of which is a cockerel hatched from one of my hens; we tried a roo early on this year and he didn't work out (he had my hens so stressed they stopped laying and he was constantly chasing them out into the road to keep them away from me but they were hand-raised and wanted no part of being kept away from us). The first egg we got after rehoming him we hatched in my son's kindergarten class so he has a special place with us and will hopefully remain with us for the long haul. I'm happy with our flock of 7 which is more than enough to provide eggs for my family but I added as many as I did so I could share with neighbors. Although, being at my personal limit to the number in my flock hasn't stopped me from looking into other breeds I'd like to get into once my two oldest have lived out their lives and bid us farewell.
How long have you been raising Hamburgs and what variety/varieties do you keep?

At first, their eggs were smallish, which I was glad about. I didn't want any eggs getting stuck. But over time, they've gotten larger. This flock will be a year old in a couple of weeks, it was our first attempt at chicken raising, so the Hamburgs have provided the bulk of our experience, we also have a Cockoo Marans roo right now that has to be kept separate from our other flock because he's HUGE, he would accidently hurt our girls since they are pretty small. And we did have a Blue Andalusian roo as well, but a bobcat got him. :-(.
We are scheduled to get 26 chicks on the 27th of this month, we're getting a mix of Dark Cornish, Blue Andalusian, Leghorns, Columbian Wyandotts, Australorps and Delawares. Our Cuckoo Marans roo needs some friends.

He was a rescue that was malnourished and had a severe infestation of lice, so he's been healing and getting stronger, by the time he's ready to integrate into a flock again, the new girls should be big enough to hang out with him.