They become mature like humans do. They start having children around 40.
Age. Gnomes mature at the same rate humans do, and most are expected
to settle down into an adult life by around age 40. (PHB p.36, "Gnome Traits")
Age. Humans reach adulthood in their late teens [...] (PHB p.31, "Human Traits")
Sadly, I couldn't find when they stop reproducing in 5e. However in 5e they age similarly to how they did in 3.5e.
Race Middle Age Old Venerable Maximum Age
Gnome 100 years 150 years 200 years +3d% years
(from the 3.5e SRD)
If it is not a problem to use 3.5 source, they would stop reproducing around 100 years(the risk of having unhealthy child is bigger with middle aged parents).