Contracting 行っておいで to

Grammar: Colloquial and Casual Speech » Contracting 行ってお出で to 行っといで

行(い)っておいで, a casual way to send someone off, may contract to 行(い)っといで.

Examples

Going to say good morning with 行っといで

Manga panel from ストロボ・エッジ showing example of Going to say good morning with 行っといで.
ストロボ・エッジ » Volume 2 » Page 15

Ninako confessed her feelings to Ren, even knowing he already has a girlfriend and would turn her down. After not seeing Ren during summer break, Ninako wonders if she’ll still be able to greet him normally. After a boy she turned down greets her normally, Ninako feels more confident.

つかさ:
「ホラっ 仁奈子(になこ) 今度(こんど)はあんたの番(ばん)だよっ」
“Hey, Ninako, now it's your turn.”
「そろそろ連(れん)くん 来(く)るんじゃない?」
“Won't Ren being coming soon?”
「行(い)っといで!!」
“Go for it!!”