Your goats were born in spring 2016? - so are now actually goatlings and not kids anymore.
Goats are seasonal breeders - they will come into season (as in ready to be mated) with the shortening days in autumn, cold weather normally helps too. With gestation - as has been said above - being 5 months you need to get organised if you want them mated this autumn. They will stop coming into season in early spring, and soon seasons are starting to get shorter, making it more difficult to get them mated if you do not have a billy on-site.
Also most breeders will take goats of around 18 months of age to the billy, commercial herds often mate kids late in their first autumn, but this requires a good eye for feeding, as the goat is still growing her own body as well as any kid(s) inside.
A goat is too fat if you cannot feel the vertebraes on her back (just in front of her hips) and you struggle to feel the ribs. Goatlings are indeed often quite fat, and I would take them off any concentrate (over a few days if they are indeed still on them) and only have hay, and grazing if they still go outside in winter. they will then need gradual increasing their concentrate feed again in the last 6 weeks before kidding to come up to milking rations.
Have you observed them when in season? If you haven't noticed and "in-season" behaviour you should get a billy rag (piece of cloth rubbed on a nice smelly boy), which if offered to sniff to a gat in season will give her characteristic tail wag, if not in season she will just try and eat it..
Are you vaccinating with Lambivac (and maybe also Ovipast)? This maybe the "shots" the vet is talking about.
Are your girls registered with the BBGS?
If you are planning to mate them to a billy not on your holding you need to enquire about CAE status requested (or not) by the stud owner.
Do you have a trailer to bring a goat in season to a billy? If you can - it may be easier to get a billy to come and reside with you for a few weeks, gets around the standstill issues and means he will detect when the girls are in season and get on with the job.
What goatbooks have you got? Kackenzie's "Goat husbandry" is really good, 5th edition is the latest.