Is "Here's wishing xxxx" proper?

The OED tells us that, in formulas used in drinking healths, here’s is elliptical for here's a health to, typically in Here’s to X. Analogous expressions do not always allow such an interpretation: the OED’s citations include Here's luck, Here's how and Here's hoping. However, it is perhaps unsurprising that the usage should be transferred in this way, given the benevolent intent common to all, including the greeting in your example.

One of the best-known uses of the formula is Rick’s in ‘Casablanca’, Here’s looking at you, kid, but he was not the first to say it. Earlier instances are found in Lowry and Hemingway.

I found that the expression here's to is used as a toast to the health, success etc of someone or something, a salutation and I suppose than also in this case is used as wish but fr a birthday.