20-45 minutes for one nap is perfectly normal and right for a 10 week old. You don't need to be expecting naps any longer than 45 minutes as a general rule.
If your baby has not yet learnt to go to sleep, it may take some time for her to simply just learn to sleep well. This is not something that comes naturally to children, they have to learn.
The EASY Routine (Eat, Activity, Sleep, You) works well at this age and is worth trying, to help develop good sleep habits. Over tiredness may be causing some issues. Here is an example 90 minute routine:
- E for Eat - Give a full feed. Takes around 15 minutes
- A for Awake Activity. Play or go somewhere, this is awake/happy time. 30 minutes or shorter if tired signs shown.
- S for sleep. Into bouncy chair 45 minutes after starting the feed. Bounce/dummy back to sleep for any wake ups until it is 90 minutes since you last started the feed. Then leave baby until she naturally next wakes and start the routine again.
- Y for You Time (but really it is just to make a nice acronym!)
My DD was on the 90 minute cycle from 6-12 weeks, then a 2 hourly routine from 3 to 5 months, with the added half hour as awake time mostly, sometimes sleep. Your baby is just at the transition between the two so could fit into either, whatever timing suits your baby. The joy of EASY is how flexible it is, whilst still allowing for predictability and structure through the daytime.
Establishing good quality, frequent sleep and good quality, frequent feeding is all that matters at this age. These are the only thing you need to focus on, don't worry about the hows and whys just yet.