Of American-English origin, the colloquial phrase bright-eyed and bushy-tailed means alert and lively.

It originated in the conventional image of a healthy, spirited squirrel or other animal; the following, for example, is from A Bunch of Golden Rod, published in The Daily Picayune (New Orleans, Louisiana) of Sunday 4^th November 1888:

The hunting season had just opened, and my heart was an open wound that bled afresh at every crack of the hunter’s gun that brought down one of the bushy-tailed, gray squirrels that live in our oak and hickory trees; pretty, soft, bright-eyed little creatures that only take with thankfulness what God made for them, an acorn or a nut.

On 3^rd December 1916, The Minneapolis Sunday Tribune (Minneapolis, Minnesota) published in its children’s section a story titled Tommy Snooks and Bessie Brooks, containing:

They played together all afternoon and when it was time for Bessie to go home Tommy walked down the road with her. When they came to the old oak tree there was a rustling of brown leaves and what do you think came frisking out of the post office and up the tree? The dearest little bright eyed bushy tailed squirrel. He ran so fast that Bessie and Tommy could only see his bushy tail.

Likewise, the following is from The Philadelphia Inquirer (Philadelphia, Pennsylvania) of Monday 29^th November 1920:

Mr. Bright-Eyed, Bushy-Tailed, Soft-Coated Gray Squirrel
sits high up in his leafless tower, laughing at the last robins as they take leave of their old haunts among the forest trees to make their long flight southward.
During the Summer time the squirrel frisks and frolics within the foliage of the woods, safe from forbidden gunners. When Winter comes he hides and sleeps in his snug storage house of food in the hollow of the tree, where he has a goodly store of nuts and grains to last him until the snow and cold have gone.
But, Mr. Squirrel is a selfish old thing who does not care to share his good things, not even at holiday times.

The collocation of bright-eyed and bushy-tailed has been used to describe other animals; in the following from The Democratic Herald (Charleston, Mississippi) of Thursday 22^nd May 1902, these adjectives qualify a rabbit:

Mr. Charles H. Broome, of Memphis, […] has with him an excellent target rifle, with which he fells to the earth both “birds of the air and beasts of the field.” […] A few evenings ago he went out armed with the beautiful specimen of the gunmaker’s art, bent upon procuring the ingredients for a Brunswick Stew, and returned in an incredibly short time, having killed three fine, fat reptiles, a bright eyed, bushy tailed bunnie, and a chicken belonging to one of his neighbors.

And, in The Pittsburg [sic] Post (Pittsburgh, Pennsylvania) of Sunday 17^th April 1904, Ernest Harold Baynes described a “little red fox” as a

bright-eyed, sharp-nosed, bushy-tailed little rascal.

The earliest figurative use of bright-eyed and bushy-tailed that I have found is from Lively Lifeboat, published in The Sunday Sun (Baltimore, Maryland) of 28^th July 1940:

Down at Arundel Cove the other day the Coast Guard tested this new all-metal welded, self-righting, self-bailing lifeboat in the presence of a trial board. Here it is being turned over so that it can show off for the visiting nautical expert.

There were no hands to abandon ship, but just stand by and watch what happens. Over the boat goes under the urgings of the crane and then up she comes again all bright-eyed and bushy-tailed, making a complete recovery in five seconds.

In The Fauna Of Texas, published in The Evening Sun (Baltimore, Maryland) of Monday 24^th January 1944, Caroline Shelton used the phrase playfully by applying it to the rattlesnakes, and conflated it with the synonymous full of beans:

The cold weather, when it does come, has one advantage. It discourages the rattlesnakes. Not that the rattlesnakes actually hibernate, because given a few warm sunny days, such as Christmas, they emerge bright-eyed, bushy tailed and full of beans.

Another early instance is from Smiling Jack, a comic strip by Zack Mosley (1906-93), published in The Salt Lake Tribune (Salt Lake City, Utah) of Tuesday 28^th March 1944:

My, but you are bright-eyed and bushy tailed today, Wagon-Wheels!
Yes, sir—Now that we kin go on to Ridgeville, Ah’ll get to meet th’ li’l tower wac with th’ sweet voice.