What you describe is pretty much what I did too. I'm a first time parent too and I think it's all you can really do. Try to put her on the tummy like you are doing to give her opportunity to be mobile, but I don't think there's anything out there that will make a baby more occupied for longer than that (aside from sleeping of course! :). My DS is 8+ months now and will play with toys for a few minutes at a time or in the jumper for a few minutes at a time, but even now it's nothing longer than that. I think that's just the name of the game for a while until they get a bit older.
I remember from 2-6 months being so bored with the routine.. and that routine day after day being feed, nap, change diaper, swing, bumbo, feed, nap, change diaper, swing, bumbo.. you get the picture.. I managed to cook dinner by moving the swing into the kitchen and talking to him about what I was cooking and trying to keep him as interested as possible without having him realize that he's been in the swing for a whole 16 minutes! :) If I got lucky he'd fall asleep every now and then. The time right before he started sitting on his own was the hardest because he started to want to wiggle out of the swing but I couldn't put him down either. During that time I found that baby wearing was the most useful. I wish I could do it now still but he's now outgrown most baby carriers. At 4 mo my DS liked playing with rattles so maybe try to giving her things like that to look, hold and so she can feel different textures.