Is there a grammar book similar to Wheelock's Latin, but for Old English?
And also, is there an equivalent of Lingua Latina Per Se Illustrata?
When I took Old English as an undergrad we used Bright's Old English Grammar & Reader, which gives a decent start. I'm sure there are other beginning books you can find, perhaps on Amazon.
Understand, though, that you immediately plunge into literature, and the survey of the grammar is designed to get you reading—for that is about all there is to do with Old English. In the second semester of the survey course we were already reading Beowulf, the crowning achievement of Old English lit.
There isn't a lot else. Compared to Latin, say, the quantity of original texts available is something on the order of a corner store in a rural town to a Whole Foods in Los Angeles. It's possible, for example, to read the entire Anglo-Saxon Chronicle in a few hours. There are poems, collections of riddles, and so forth, but the sad fact is that we simply don't have a wealth of OE lit bulging the stacks. Some of it you will only see as fragments in places like the British Museum (I recall an interesting set of glazed tiles that formed a kind of "comic book" about the exploits of the boy Jesus, for example) and, if you're lucky enough to get access, in the stacks of academic libraries. If your aim is to be an Old English dilettante, you are going to have to reckon with rather more work than may be comfortable for you.
Moreover, the grammar "skeleton" you receive going into your reading will constantly prove insufficient to explain some of the constructions you'll encounter, and you'll wonder if anomalies you see are regional variations or part of a more complicated grammar you aren't privy to or transcription errors—or all three. Such questions, if answerable at all, can require serious scholarship to resolve. You will have to read far more modern English about the works than you will read the Old English works themselves. (The good news is that probably most questions you will have about the text are answered by annotations.)
When I studied this as an undergraduate, we used Sweet's Anglo-Saxon Primer. It's a long time since I read any of it, and language teaching has come on in leaps and bounds since then, but it seemed to do its job, and it taught me some Old English.