R/C batteries.

I have been building scale sailing models for many years for collectors
and museums but with the advent of our first grandson I have decided to
build a fully detailed R/C model of the trawler 'Ladysmith' at 1/48
scale for him to take down the local boat pool when he is older which is
only five minutes walk from his house (lucky blighter).
Thing is I only know the basics of R/C and am somewhat confused as to
how long batteries last and motor sizes etc, I have a nice 545 motor and
a slightly used 540 and some other stuff but my need is for battery info
i.e how long would a 12v 1.2 Ah battery power a 545 motor or am I better
off going for a larger battery.
As this is a trawler of 1905 vintage I dont want it taking off like a
Seacat so need to keep the revs in order, what is the best way to do
this and the approximate screw rpm for a 2'' prop with the 545 behind it
for the speed to look realistic?, I am also looking at building a sea
going tug of the 1920 - 40 era later if anyone has any suggestions,
many thanks, Terry