What's the opposite of “last-minute (Christmas) shopping”?

This year I am doing my shopping at the first opportunity.

: as soon as it is possible for someone to do something

Merriam Webster

This will be the first opportunity for the two leaders to take the measure of the other in person

'CSIS on Donald Trump' - 2018

It was the first opportunity to welcome the University’s ‘Think Big’ scholars

Bristol Universtity - 'International Scholars - 13 Oct 2018

"This year, I'm doing my shopping proactively."

From the Merriam-Webster definition of proactive:

2 [ ²pro- + reactive ] : acting in anticipation of future problems, needs, or changes

"This is the person you need to talk to, she's a real go-getter."

: an aggressively enterprising person

So, you could say:

She's a real go-getter. She even does her shopping proactively!

Maybe, "I did my Christmas shopping pre-season."

Adding “bird” to “early” (= “early bird”***) would at least provide a figurative, if not slangish, option and I imagine that one of the benefits of/reasons for being an “early bird”/”early-bird shopper” is avoiding the last-minute (Christmas/shopping) rush.

Using this notion of “early bird” to answer the respective parts of your question could take the following forms:

(1) This year, I'm doing my Christmas shopping early-bird style.

You could also use a variation of this figurative notion in a modified version of Part 1 by expanding trendwatching.com’s term “early birding” beyond its original, online “pre-ordering/pre-purchasing” meaning:

(1.1) This year, I'm early-birding my Christmas shopping.

(2) This is the person you need to talk to, she's an expert early birder when it comes to planning [important events/holidays/exams].

*** an early bird

1. …

2. If you call someone an early bird, you mean that they succeed in doing something before other people. Florida has been an early bird in terms of presidential voting for some time.
   Note: Early-bird can also be used to describe things that are available to these people. An early-bird discount is sometimes available at the beginning of the season.

(from Collins COBUILD Idioms Dictionary, 3rd ed. © HarperCollins Publishers 2012, via thefreedictionary.com)

An unnecessarily formal term used in this context would be somewhat idiomatic (but not really slang, I guess):
This year, I'm doing my Christmas shopping posthaste.
This year, I'm doing my Christmas shopping stat.
This year, I'm doing my Christmas shopping with all due urgency.