Absolutely!
The best process is to use iTunes to do this:
(1) make a backup of the iPad1 before you even plug the new iPad (remember the time); then disconnect the iPad1 from iTunes
(2) Plus in the new iPad and follow along as iTunes starts setting it up for you (just keep following the prompts and clicking "stuff")
(3) Eventually, iTunes will ask you whether to set the iPad up as new or restore from backup. Elect to "restore from backup" and then pick that fresh iPad1 backup you made (which is why you wanted to remember the time). iTunes will finish doing its magic and, when it's done, you should have a new iPad that looks like the old. Well, except it'll be new ... with a retina screen ... and screamingly fast.
Hopefully, that's what happens. Holler back if you have troubles. And, congrats on the [coming from Santa] new iPad.
Marilyn