I found something that works!
pkg> add https://github.com/chriswaudby/LsqFit.jl.git#MeasurementsExtension
For example
using LsqFit, Plots, Measurements
@. gauss(x,p) = p[1] + p[2] * exp(-(x-p[3])^2/p[4]^2)
x = range(-1,1,100)
yerr = gauss(x,[0,1,0,0.5]) + 0.1*randn(length(x)) .± 0.1
fit = curve_fit(gauss, x,yerr,Float64[0,1,0,1])
begin
scatter(x,yerr)
plot!(x,gauss(x,fit.param);ribbon = gauss(x,fit.param.+stderror(fit)) - gauss(x,fit.param.-stderror(fit)))
end
savefig("fit.png")
