I will tell you what I do, and have done for many years regarding breeding. Unless the female was particularly well grown (and I have had one or two big youngsters) I would always wait until they were 15-18 months before breeding. If you are taking your female to a good goat owner, it is more than likely they will want to serve her in hand i.e. supervise the mating rather than just you leave your nanny and let her run with the billy. If this is the case, they will ask you to bring the female as soon as she is definitely in season. She will take you, once she gets a whiff of the billy ......so hold on to your rope
They will bring the billy out to the female, let him sniff her, and if she is definitely in season, he will be there. Its very quick, blink and you will miss it!! Doing it this way, minimises the risk of any damage to your goat with horns or otherwise.
So, the question of who has horns does not really matter.
If you let your female run with the billy and leave her there, then there is the issue of horns hurting another goat. Personally, as she is young, and its her first mating, I would opt to have her served under supervision. Once done, you take her home and wait three weeks - and be prepared for the smell to linger on everything. Watch carefully for signs of coming in season again, if she does, the billy owner will hopefully give you a free go this time!!
I would definitely take your female to the billy in the Autumn she will be big enough to cope.
Many years ago, when I took my first female goat to the billy, she was only 15 months old, and the most enormous British Sanaan male came out of his stable......He was about three times the size of poor Penny, and I was certain his weight would kill her, but it didn't and the resulting kids were the enormous ones mentioned above, who matured very quickly.
As to your current milker, some do milk through, although they will never milk as good that second year, especially during the winter months, so I would not expect gallons of milk.