The only thing that really matters is that you read with her regularly as part of a bedtime or playtime routine.
If you find a way to make the laptop work for you so that you both can read it together comfortably before bed, that is excellent. Books themselves are so much less important than enjoying reading that it doesn't even compare. There is no harm at all in using the laptop and if it doesn't work, trying something else.
With that said, for learning to read at the infant level, books are probably better (see below), and there are cheaper options than buying new that you can easily take advantage of.
If you don't have much money, my recommendation is to seek out local public libraries, charities, and parent's groups.
Public libraries are free except for the time cost (and the children's section is a great place to take your child, just as a meeting area), and local charity stores (at least in the UK) normally have a books section where the books are going for literal pennies. If that's below your threshold (and even if it's not), you probably qualify for a free book scheme like Booktrust (if you're in the US, I found this list of potential charities that do the same stuff).
As for parent's groups, if someone in our children's group was looking for books, we'd be happy to offload a library's worth of books we no longer need for our daughter (besides promoting reading, we could use the space). Ask around. Anyone who's moving or whose child has grown out of their baby books will jump at the chance to do something positive with them.
In terms of your original question, there are several issues with replacing children's books with ebooks.
One is that for the very young or those who are just learning to read, the tactile sensation of turning pages makes books attractive. This is probably the least relevant in some ways, as kids also love buttons for the interactivity, but it matters. You can trace words on a page in a way that you don't really on a computer screen.
The second is that children's books are generally big, bright, bold pictures and small amounts of text per page. This isn't what dedicated e-readers are designed to do, and the ebook market reflects that. Books for the very young or early readers simply don't come out on Kindle etc. The only device that successfully compares is the iPad, and that's just too expensive. (Although the Reading Rainbow app is apparently excellent).
And unless you're using a dedicated e-reader like a Kindle or a Nook, the light coming out of a computer screen makes it hard to read for long periods. Couple that with the low resolution of most computer screens, which has a far greater relative effect on text than on pictures, and you get a very poor reading experience. That could well have an effect on how comfortable they are with reading, and how much they look forward to/avoid it.
And a laptop isn't a great reading experience anyway. I can curl up in a chair with a Kindle quite happily, but my laptop really requires me to be sitting at a desk. I can't carry my laptop around like I do a book.
Another issue is that the computer will never be "hers", and a book can be. I've come in to find my daughter leafing through one of her books saying "Readingreadingreading". That's wonderful. If I came in to find her punching the buttons on my laptop saying the same, not so much. The books can stay in her room, they can be available when I need to work on the laptop, they are in essence her books which I read to her until she's ready to read. That has an effect.
But the most critical is that laptops do more interesting things. If you're using the same device for videos and for reading, you may well find that your child doesn't want to read when the computer could be showing Spongebob instead. And she will want to press the keys, which is far more interruptive than when she tries to turn the pages of a book.
Also, in terms of expense, my daughter has trashed at least one e-Reader already and has changed settings on my laptop I didn't even know existed (who knew Vista could turn the screen sideways if you hit the correct key sequence?), but her best attempts to destroy books have been easily countered with some tape, and nothing significantly damages a cardboard baby book, not even drowning it in the bath. I've returned children's books to the library with pages taped back in and they've been fine with it, it's budgeted for. Your savings on books may be replaced by a catastrophic expense when she pulls your laptop off the table for "stories".
Regarding age, the tactile stuff is less relevant to a child that's already happy and comfortable with reading, although some studies suggest paper-based information is more easily retained. A 10-year old is likely to be as happy with a screen as with a printed page.
But as I said at the start, the important thing is to make regular reading something your child is comfortable and happy with, and that they associate reading with that experience. What they read is far less relevant, and what they read it even less. And the best way to do that is to read with her.