cisco routers store there configs in a plain txt file. you can copy this txt file over a tftp link between the router to a computer or router to router. if you connect via a console port with telnet then its easier to simply backup this config to your desktop and push it out to another router. since you are replacing with a higher version you may need to modify the configs a bit to account for feature changes.
before you can push such a config you need to set a base config on the router. to do this you want to start the new router and do NOT do the config wizzard. just say no and it will bring you to a user prompt with a > this is a user level access, to config anything you need elevated access indicated by a # symbol. you need to setup passwords and terminal access before it will let you push a config. from the > you type en (enable) then config t to config an interface port that is pluged to the other router. you must set config e/1 (ethernet 1) ip address by typing: config e/1, ip address XXX.XXX.XXX.XXX XXX.XXX.XXX.XXX (the second set is subnet mask) then after hitting enter type "no shut" this will put the line to up. the ip address must be on the same subnet for this way to work. an easier way for you may be to log into one router via telnet (using the seriel port on your comp and console port on your router) and save the config to a txt file, then log into the new router and upload this same config using the same config. there are hundreds of commands so i would recommend just youtubing or googling a quick video on this. if you are a cisco acad guy then you can go to cisco.netacad.net and log in to get very well laid out guides on how to do this. dont forget to do a copy run start to save your running config to yoru startup config.