I found one terminal which supports dotted patterns: the lua tikz terminal:
set terminal lua tikz standalone
set output 'dot-pattern.tex'
set boxwidth 0.8 relative
set samples 10
unset key
set yrange [0:11]
plot '+' using 1:($0+1) with boxes lt -1 lw 2 lc rgb '#990000' fillstyle pattern 8
set output
system('pdflatex dot-pattern.tex')

With this you could also use custom fill patterns by overwriting a predefined pattern:
set terminal lua tikz standalone header '\tikzset{gp pattern 8/.style={pattern=mypatterh}}'
and you must define a custom pattern, like shown in
Custom and built in TikZ fill patterns.
Using black borders and colored fill pattern is possible with
plot '+' using 1:($0+1) with boxes lc rgb '#990000' fillstyle pattern 8 noborder,\
'+' using 1:($0+1) with boxes lt -1 lw 2
testcommand. - Christoph