Dell do not actually make their own printers but rebrand/rebadge existing models from printer's manufacturers such as Lexmark, Samsung or Canon.
Eg: Dell All-In-One 966 which is in fact a Lexmark All-In-One X9350 and for which Lexmark Mac OS driver work perfectly. Well, the wired/wireless printing works... but I could never get the wireless scanner to work under Mac OS though.
In the case of the Dell 1110, the actual hardware is a Samsung ML-2010
for which there are Mac OS drivers...
I can't say if it'll work straight away after drivers are installed and printer added through Printer Pref Pane.
What I can say though, is that in the case of the Dell AIO966/Lexmark X9350, the process to install the printer under Mac OS is to start with the Lexmark driver installation, then use CUPS Administration
to add the printer. It'll never work if printer is added directly through Printer Pref Pane.